Chapter 8 Resource Masters

Transcription

1 Chapter Resource Masters

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3 Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Stud Guide and Intervention Workbook Stud Guide and Intervention Workbook (Spanish) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Answers for Workbooks The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. Spanish Assessment Masters Spanish versions of forms A and C of the Chapter Test are available in the Pre-Algebra Spanish Assessment Masters ( ). Copright b The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced onl for classroom use; be provided to students, teacher, and families without charge; and be used solel in conjunction with Glencoe Pre-Algebra. An other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 77 rion Place Columbus, H 0 ISBN: Pre-Algebra Chapter Resource Masters

4 CNTENTS Vocabular Builder...vii Lesson - Stud Guide and Intervention...7 Skills Practice... Practice...9 Reading to Learn Mathematics...0 Enrichment... Lesson - Stud Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson - Stud Guide and Intervention...7 Skills Practice... Practice...9 Reading to Learn Mathematics...0 Enrichment... Lesson - Stud Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson - Stud Guide and Intervention...7 Skills Practice... Practice...9 Reading to Learn Mathematics...0 Enrichment... Lesson - Stud Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson - Stud Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson -9 Stud Guide and Intervention...7 Skills Practice... Practice...9 Reading to Learn Mathematics...0 Enrichment... Lesson -0 Stud Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Chapter Assessment Chapter Test, Form...7 Chapter Test, Form A Chapter Test, Form B Chapter Test, Form C Chapter Test, Form D Chapter Test, Form Chapter pen-ended Assessment...79 Chapter Vocabular Test/Review...0 Chapter Quizzes &... Chapter Quizzes &... Chapter Mid-Chapter Test... Chapter Cumulative Review... Chapter Standardized Test Practice... Unit Test/Review (Ch 7 )...7 Standardized Test Practice Student Recording Sheet...A ANSWERS...A A7 Lesson -7 Stud Guide and Intervention...7 Skills Practice... Practice...9 Reading to Learn Mathematics...0 Enrichment... iii

5 Teacher s Guide to Using the Chapter Resource Masters The Fast File Chapter Resource sstem allows ou to convenientl file the resources ou use most often. The Chapter Resource Masters includes the core materials needed for Chapter. These materials include worksheets, etensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Pre-Algebra TeacherWorks CD-RM. Vocabular Builder Pages vii-viii include a student stud tool that presents up to twent of the ke vocabular terms from the chapter. Students are to record definitions and/or eamples for each term. You ma suggest that students highlight or star the terms with which the are not familiar. When to Use Give these pages to students before beginning Lesson -. Encourage them to add these pages to their Pre-Algebra Stud Notebook. Remind them to add definitions and eamples as the complete each lesson. Stud Guide and Intervention Each lesson in Pre-Algebra addresses one or two objectives. There is one Stud Guide and Intervention master for each lesson. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice There is one master for each lesson. These provide computational practice at a basic level. When to Use These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. Practice There is one master for each lesson. These problems more closel follow the structure of the Practice and Appl section of the Student Edition eercises. These eercises are of average difficult. When to Use These provide additional practice options or ma be used as homework for second da teaching of the lesson. Reading to Learn Mathematics ne master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the contet of and relationships among terms in the lesson. Finall, students are asked to summarize what the have learned using various representation techniques. When to Use This master can be used as a stud tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. Enrichment There is one etension master for each lesson. These activities ma etend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics the are learning. These are not written eclusivel for honors students, but are accessible for use with all levels of students. When to Use These ma be used as etra credit, short-term projects, or as activities for das when class periods are shortened. iv

6 Assessment ptions The assessment masters in the Chapter Resource Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment Chapter Tests Form contains multiple-choice questions and is intended for use with basic level students. Forms A and B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Forms C and D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with aes are provided for questions assessing graphing skills. Form is an advanced level test with free-response questions. Grids without aes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. The pen-ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. A Vocabular Test, suitable for all students, includes a list of the vocabular words in the chapter and ten questions assessing students knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. Intermediate Assessment Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions. Continuing Assessment The Cumulative Review provides students an opportunit to reinforce and retain skills as the proceed through their stud of Pre-Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which ma appear on the standardized tests that the ma encounter. This practice includes multiplechoice, grid-in, and open-ended questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 0. This improves students familiarit with the answer formats the ma encounter in test taking. The answers for the lesson-b-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer kes are provided for the assessment masters in this booklet. v

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8 NAME DATE PERID Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of ke vocabular terms ou will learn in Chapter. As ou stud this chapter, complete each term s definition or description. Remember to add the page number where ou found the term. Add these pages to our Pre-Algebra Stud Notebook to review vocabular at the end of the chapter. Vocabular Term Found on Page Definition/Description/Eample Vocabular Builder best-fit line boundar constant of variation VEHR-ee-AY-shuhn direct variation function half plane linear equation LIHN-ee-uhr vii

9 NAME DATE PERID Reading to Learn Mathematics Vocabular Builder (continued) Vocabular Term rate of change Found on Page Definition/Description/Eample slope slope-intercept form IHNT-uhr-SEHPT substitution sstem of equations vertical line test -intercept -intercept viii

10 - NAME DATE PERID Stud Guide and Intervention Functions Function A special relation in which each member of the domain is paired with eactl one member in the range. Vertical Line Test Since functions are relations, the can be represented using ordered pairs, tables, or graphs. Eample a. {( 0, ), (0, ), (0, 9), (0, )} Domain () Move a pencil or straightedge from left to right across the graph of a relation. If it passes through no more than one point on the graph, the graph represents a function. If it passes through more than one point on the graph, the graph does not represent a function. Determine whether each relation is a function. Eplain. Range () 9 Because each element in the domain is paired with onl one value in the range, this is a function. b Domain () Range () 9 Because 0 in the domain is paired with and in the range, this is not a function. Lesson - Eercises Determine whether each relation is a function. Eplain.. {(, ), (, ), (, 7), (, 0)} No; in the domain is paired with and 0 in the range.. {(, 7), (, 0), ( 0, 0), (, 0), (, 0)} Yes; each value is paired with onl one value Yes; each value is paired with onl one value. No; in the domain is paired with and 7 in the range. Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

11 - NAME DATE PERID Skills Practice Functions Determine whether each relation is a function. Eplain.. {(, ), (, ), (, ), (, )} No; in the domain is paired with and in the range.. {(, ), (, ), (0, ), (, )}. Yes; each value is paired with onl one value. 0 Yes; each value is paired with onl one value.. {(0, ), (, ), (, ), (, )} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (0, )}. Yes; each value is paired with onl one value. 0 Yes; each value is paired with onl one value No;. in the domain is paired with. and. in the range. Yes; each value is paired with onl one value Yes; an vertical line passes through no more than one point of the graph. No; a vertical line passes through more than one point... No; a vertical line passes through more than one point. Yes; an vertical line passes through no more than one point of the graph. Glencoe/McGraw-Hill Glencoe Pre-Algebra

12 - NAME DATE PERID Practice Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. No; in the domain is paired with and in the range. 0 No; in the domain is paired with and 0 in the range.. {(, ), (, ), (, ), (, ), (, )} Yes; each value is paired with onl one value.. {(, ), (, ), ( 7, ), (, ), (, ), ( 7, )}. No; 7 in the domain is paired with and in the range Yes; each value is paired with onl one value. Lesson No;.0 in the domain is paired with. and.7 in the range. No; in the domain is paired with and in the range. EMPLYMENT For Eercises 9, use the table, which shows the percent of emploed men and women in the U.S. labor force ever five ears from 90 to Is the relation (ear, percent of men) a function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed men. 0. Describe how the percent of emploed men is related to the ear. The number of emploed men varies each ear, but is around 7 percent of the male population. Year Emploed Members of Labor Force Men Women (% of male (% of female population) population) Source: U.S. Census Bureau. Is the relation (ear, percent of women) a function? Eplain. Yes; each ear is paired with onl one value for the percent of emploed women.. Describe how the percent of emploed women is related to the ear. As the ears progress, the percent of emploed women increases. Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

13 - NAME DATE PERID Reading to Learn Mathematics Functions Pre-Activit How can the relationship between actual temperatures and windchill temperatures be a function? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. n grid paper, graph the temperatures as ordered pairs (actual, windchill). b. Describe the relationship between the two temperature scales. Sample answer: As the actual temperature increases, the windchill temperature also increases. c. When the actual temperature is 0 F, which is the best estimate for the windchill: F, F, or 0 F? Eplain. F; when the actual temperature decreases, the windchill temperature also decreases Reading the Lesson. See students work. Write a definition and give an eample of each new vocabular word or phrase. Vocabular Definition Eample. function. vertical line test. For a relation to be a function, each element in the domain must have onl one corresponding element in the range.. Eplain what is meant b the phrase distance is a function of time. Sample answer: How far something travels depends on how much time elapses. Helping You Remember. You have learned various was to determine whether a relation is a function. Choose which method is the easiest for ou to use, then write a few sentences eplaining how that method relates to the other methods. Sample answer: Placing the range values in a table with their corresponding domain values makes it eas to see whether an element in the domain is paired with onl one element in the range. B graphing and connecting the points, the vertical line test can be applied to arrive at the same answer. Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

14 - NAME DATE PERID Enrichment Emm Noether Emm Noether ( 9) was a German mathematician and a leading figure in modern abstract algebra. Her contributions helped change the role of women in German universities and advanced the mathematical progress of the time. Noether fought and overcame rules that once prevented her from becoming a facult member. Her most notable work pertains to linear transformations of non-commutative algebras and their structures. A linear equation is an eample of a transformation, unless it is the equation for a vertical line. In a transformation, a given rule transforms each number in one set, the domain, into one and onl one number in another set, the range. In graphing linear equations, the domain is usuall the set of real numbers and the range is either the set of real numbers or a subset of the real numbers. Each value of is transformed into some value of. Transformation f is shown in the diagram below. The transformation takes each element of the domain {,, } and adds to produce the corresponding value in the range. Functional notation is used to show the rule f (). Lesson - f() f f() Use functional notation to write the rule for each transformation.. g(). h() g 7 h g(). What do ou think is a non-commutative algebra? a b b a for some a, b R h( ). Eplain whether the diagram below shows a transformation. 7 9 No, the number corresponds to more than one value in the range. Glencoe/McGraw-Hill Glencoe Pre-Algebra

15 - NAME DATE PERID Stud Guide and Intervention Linear Equations in Two Variables A function can be represented with an equation. An equation such as.0 is called a linear equation. A linear equation in two variables is an equation in which the variables appear in separate terms and neither variable contains an eponent other than. Linear Equations,, Nonlinear Equations,,, Solutions of a linear equation are ordered pairs that make the equation true. ne wa to find solutions is to make a table. Eample Eample Complete the table. Use the results to write four solutions of 0. Write the solution as ordered pairs. 0 (, ) ( ) 0 (, ) 0 (0) 0 0 (0, 0) () 0 (, ) () 0 (, ) Eercises A linear equation can also be represented b a graph. The coordinates of all points on a line are solutions to the equation. Graph 0 b plotting ordered pairs. Plot the points found in Eample. Connect the points using a straight line. (, ) (, ) 0 (0, 0) Find four solutions of each equation. Write the solutions as ordered pairs.. Sample answers are given (, ), (0, ), (, ), (0, 7), (, 9), (0, ), (, ), (, ) (, 0), (, ) (, ), (, ) Graph each equation b plotting ordered pairs.... Glencoe/McGraw-Hill Glencoe Pre-Algebra

16 - NAME DATE PERID Skills Practice Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs. 9. Sample answers are given.. =.. (, ), (0, ), (, ), (0, ), (, 7), (0, ), (, ), (, ) (, ), (, 0) (, ), (, ).. 7. (, ), (0, ), (, ), (0, ), (, ), (0, ), (, ), (, 7) (, ), (, ) (, ), (, ) (, ), (0, ), (, ), (0, 0), (, ), (0, ), (, ), (, ) (, ), (, ) (, 0), (, ) Graph each equation b plotting ordered pairs Lesson Glencoe/McGraw-Hill Glencoe Pre-Algebra

17 - NAME DATE PERID Practice Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs.. Sample answers are given (, ), (0, ), (, 7), (0, 7), (, ), (0, ), (, ), (, ) (, 7), (, 7) (, ), (, )... 7 (, 7), (0, ), (, ), (0, ), (, ), (0, ), (, ), (, ) (, ), (, ) (, 7), (, 0) Graph each equation b plotting ordered pairs CKING For Eercises, use the following information. Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation 0.0 describes the approimate number of ounces in grams.. Find three ordered pairs of values that satisf this equation. Sample answer: (00, ), (00, ), (00, ). Draw the graph that contains these points.. Do negative values of make sense in this case? Eplain. No; a recipe cannot contain a negative number of grams of an ingredient. Glencoe/McGraw-Hill Glencoe Pre-Algebra unces Grams

18 - NAME DATE PERID Reading to Learn Mathematics Linear Equations in Two Variables Pre-Activit How can linear equations represent a function? Do the activit at the top of page 7 in our tetbook. Write our answers below. Reading the Lesson a. Complete the table to find the cost b. n grid paper, graph the of,, and cans of peaches. ordered pairs (number, cost). Then draw a line Number of.0 Cost () through the points. Cans ().0().0.0().00.0().0.0().00 c. Write an equation representing the relationship between number of cans and cost.. or.0 Write a definition and give an eample of the new vocabular phrase. Cost ($) 0 Number of Cans Lesson -. Vocabular Definition Eample linear See students work. equation. Determine whether each equation below is linear or nonlinear and eplain wh. a. Linear; the variables appear in separate terms, and neither variable contains an eponent other than. b. Nonlinear; the variable has an eponent of. c. Nonlinear; the variables appear in the same term.. Solutions of a linear equation are ordered pairs that make the equation true. Helping You Remember. Work with one of our classmates translating linear equations into English. First, each of ou should write a linear equation. Then trade equations and take turns reading the equations in everda words. Second, each of ou should describe a line in terms of its and values. Trade sentences and translate them into linear equations. Sample answer: 0; The value of subtracted from the value of is 0. Glencoe/McGraw-Hill Glencoe Pre-Algebra

19 - NAME DATE PERID Enrichment Equations with Two Variables Complete the table for each equation Glencoe/McGraw-Hill Glencoe Pre-Algebra

20 - NAME DATE PERID Stud Guide and Intervention Graphing Linear Equations Using Intercepts Finding Intercepts The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. To find the -intercept, let 0 in the equation and solve for. To find the -intercept, let 0 in the equation and solve for. Eample Find the -intercept and the -intercept for the graph of 0. To find the -intercept, let 0. 0 Write the equation. (0) 0 Replace with 0. Simplif. To find the -intercept, let 0. 0 Write the equation. Eample (0, ) 0 (, 0) Graph 0. (0) 0 Replace with 0. Simplif. Eercises Find the -intercept and the -intercept for the graph of each equation ; none; ; Graph each equation using the - and -intercepts. Lesson (, 0) (0, ) (0, 9) (9, 0) 9 (, 0) (0, ) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

21 - NAME DATE PERID Skills Practice Graphing Linear Equations Using Intercepts State the -intercept and the -intercept of each line ; none; ; Find the -intercept and the -intercept for the graph of each equation ; 0; ; ; ; none; 7 Graph each equation using the - and -intercepts (0, ) + (, 0) (0, ) (0, ) + (, 0)... (0, ) (0, ) (, 0) (, 0) (, 0) Glencoe/McGraw-Hill Glencoe Pre-Algebra

22 - NAME DATE PERID Practice Graphing Linear Equations Using Intercepts Find the -intercept and the -intercept for the graph of each equation , none,, ,, 7, none Graph each equation using the - and -intercepts (7, 0) (0, 7) (0, ) + (, 0) (0, ) (, 0) (7, 0) (0, ) 7 + (0, ) (, 0) (, 0) Lesson -. SAVINGS Rashid s grandparents started a savings account for him, contributing $000. He deposits $0 each month into the account. The equation represents how much mone is in the savings account after number of months. Graph the equation and eplain what the -intercept means. The -intercept 000 shows how much mone was in the savings account before Rashid made an deposits. $ (thousand) Months Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

23 - NAME DATE PERID Reading to Learn Mathematics Graphing Linear Equations Using Intercepts Pre-Activit How can intercepts be used to represent real-life information? Do the activit at the top of page in our tetbook. Write our answers below. a. Write the ordered pair for the point where the graph intersects the -ais. What does this point represent? (0, ); a temperature of 0 C equals F. b. Write the ordered pair for the point where the graph intersects the -ais. What does this point represent? (, 0); a temperature of approimatel C equals 0 F. Reading the Lesson. See students work. Write a definition and give an eample of each new vocabular word. Vocabular Definition Eample. -intercept. -intercept. The -coordinate of the -intercept is 0. The -coordinate of the -intercept is 0.. Draw a model on the coordinate grid that shows how to graph a line using the -intercept and the -intercept of a line. Eplain our model. (0, ) (, 0). Is a line with no -intercept vertical or horizontal? Eplain. Horizontal; if a line has no -intercept, the line will never cross the -ais. Therefore, the line must be parallel to the -ais. Helping You Remember Sample answer: The -intercept is, which means that one point of the graph is at (, 0). The -intercept is, which means that another point of the graph is at (0, ). Graph both points on the grid and draw a line through them.. The word intercept has man snonms in English. Look up intercept in a thesaurus and find one or two snonms that help ou remember the mathematical meaning of the word. Eplain our selection. Sample answer: cut off; The -intercept is where the -ais cuts off the line; the -intercept is where the -ais cuts off the line. Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

24 NAME DATE PERID - Enrichment Curves Step Step Step Make a table of ordered pairs that satisf the equation. Graph each point. Draw a smooth curve connecting the points. If ou know the graph is going to be a straight line, then ou onl need two points (a third one as a check). But if the graph is going to be a curved line, then ou need enough points to be able to sketch a nice smooth curve. This ma be or more points. Sketch a smooth curve through the points shown. The right side of the first curve has been done for ou.... Graph each equation Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

25 - NAME DATE PERID Stud Guide and Intervention Slope Slope describes the steepness of a line. slope = r ise vertical change run Model (, ) Note that the slope is the same for an two points on a straight line. Smbols m, where rise run (, ) Eample m Find the slope of the line. Definition of slope m ( 9, ) (, ), (, ) (9, ) m (9, ) (, ) The slope is. Eercises Find the slope of each line.... (, ) (, ) (, ) (0, ) (, ) (, ) Find the slope of the line that passes through each pair of points.. A(, ), B(, ). L(, ), M(, ). R(7, ), S(7, ) undefined 7 Glencoe/McGraw-Hill Glencoe Pre-Algebra

26 - NAME DATE PERID Skills Practice Slope Find the slope of each line.... (, ) (0, ) (, ) (, ) (0, ) (0, )... (0, ) (, ) (0, ) (, ) (, ) (0, ) Find the slope of the line that passes through each pair of points. 7. A(, ), B(, 7). C(7, ), D(, ) 9. E(7, ), F(, ) 0. G(, ), H(, ). J(, 9), K(0, ). L(, ), M(, ). P(, ), Q(7, ). R(, ), S(, ). T(, ), U(, ) undefined. P(0, ), Q(, ) 7. R(, ), S(7, ). T(, ), U(7, ) CAMPING A famil camping in a national forest builds a temporar shelter with a tarp and a -foot pole. The bottom of the pole is even with the ground, and one corner is staked feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole? Lesson - 0. ART A rectangular painting on a galler wall measures 7 meters high and meters wide. What is the slope from the upper left corner to the lower right corner? 7 Glencoe/McGraw-Hill Glencoe Pre-Algebra

27 - NAME DATE PERID Practice Slope Find the slope of each line.... (, ) (0, ) (0, ) (, ) (0, ) (, ) Find the slope of the line that passes through each pair of points.. A( 0, ), B(, ). C(7, ), D(, ). E(, ), F(, ) 7 7. G(, 7), H( 0, ). J(, 0), K(, ) 9. L(, ), M(, 9) 0. P(, ), Q(, ). R(, ), S(, ). T(, ), U(, ) undefined 0. CAKES A wedding cake measures feet high in the center and the diameter of the bottom tier is inches. What is the slope of the cake?. INSECTS ne particularl large ant hill found in 997 measured 0 inches wide at the base and inches high. What was the slope of the ant hill? 9 0. ARCHAELGY Toda, the Great Pramid at Giza near Cairo, Egpt, stands 7 meters tall, coming to a point. Its base is a square with each side measuring 0 meters wide. What is the slope of the pramid? 7. BUSINESS ne warehouse uses -foot long ramps to load its forklifts onto the flat beds of trucks for hauling. If the bed of a truck is feet above the ground and the ramp is secured to the truck at its end, what is the slope of the ramp while in operation? Glencoe/McGraw-Hill Glencoe Pre-Algebra

28 - NAME DATE PERID Reading to Learn Mathematics Slope Pre-Activit How is slope used to describe roller coasters? Do the activit at the top of page 7 in our tetbook. Write our answers below. a. Use the roller coaster to write the ratio h eight in simplest form. length Reading the Lesson b. Find the ratio of a hill that has the same length but is feet higher than the hill on page 7. Is this hill steeper or less steep than the original? ;steeper Write a definition and give an eample of the new vocabular word.. Vocabular Definition Eample slope See students work. Complete each sentence.. Slope is the same for an two points on the line.. A line that slopes downward from left to right has a negative slope.. A line that slopes upward from left to right has a positive slope.. A horizontal line has a zero slope.. The slope of a vertical line is undefined. Helping You Remember 7. For each graph, draw a line with the given slope. a. Positive b. Negative c. Zero d. Undefined Lesson - See students graphs. Glencoe/McGraw-Hill Glencoe Pre-Algebra

29 - NAME DATE PERID Enrichment Investments The graph below represents two different investments. Line A represents an initial investment of $0,000 at a bank paing passbook-savings interest. Line B represents an initial investment of $000 in a profitable mutual fund with dividends reinvested and capital gains accepted in shares. B deriving the equation, m b, for A and B, a projection of the future can be made. 0 Dollars Invested 0 (thousands) A B Years Invested Solve.. The -intercept, b, is the initial investment. Find b for each of the following. a. line A 0,000 b. line B 000. The slope of the line, m, is the rate of return. Find m for each of the following.,000 0,000 0, a. line A b. line B What are the equations of each of the following lines? a. line A 0,000 b. line B Answer each of the following, assuming that the growth of each investment continues in the same pattern.. What will be the value of the mutual fund after the th ear? 77() 000 $,997. What will be the value of the bank account after the th ear? () 0,000 $,. When will the mutual fund and the bank account be of equal value? 0, ears 7. In the long term, which investment has the greater paoff? mutual fund Glencoe/McGraw-Hill Glencoe Pre-Algebra

30 - NAME DATE PERID Stud Guide and Intervention Rate of Change Rate of Change A change in one quantit with respect to another quantit slope change in change in A special tpe of linear equation that describes k, where k 0 rate of change Direct Variation and both increase or both decrease at the same rate varies directl with. Slope, or rate of change, k, is called the constant of variation. Eample rate of change slope Find the rate of change for the linear function represented in the table. c hange chang in e in or For each time increase of h, the temperature increases b C. Time (h) 0 Temperature ( C) 0 Eample Write an equation relating and from Eample. Step Find the value of k. Step Use k to write an equation. k Direct variation k Direct variation k() Replace with and with. Replace k with. k Simplif. Eercises. Find the rate of change for the linear function. increase of 00 mph Time (h) 0 Distance Flown (mi) Suppose varies directl with. Write an equation relating and.. when 7. when. when Lesson - Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

31 - NAME DATE PERID Skills Practice Rate of Change Find the rate of change for each linear function.. 0. Amount of Milk (L) increase of L/ wk. 00. Savings ($000) Week Year Salar ($),000,00,000,00 increase of $00/ear Month Number of Emploees Year decrease of $000/ear increase of emploees/month Suppose varies directl with. Write an equation relating and.. when 7. when 7. when 7. when 9. when 0. when.. when. 9 when. when 0.. when. when. when 7 9 Glencoe/McGraw-Hill Glencoe Pre-Algebra

32 - NAME DATE PERID Practice Rate of Change Find the rate of change for each linear function.. 0. Air in Tires (psi) Time Distance (h) (km) Time (min) decrease of psi/min increase of 0 km/h Suppose varies directl with. Write an equation relating and.. when. 7 when 9. when. 0 when 7. when 7. when 9.. when 9 0. when. when 0.. when 7. when. when 9 TRAFFIC MANAGEMENT For Eercises and, use the following information. San Diego reserves epress lanes on the freewas for the use of carpoolers. In order to increase traffic flow during rush hours, other drivers ma use the epress lanes for a fee. The toll varies directl with the number of cars on the road. The table shows a sample of possible tolls.. Write an equation that relates the toll and traffic volume.. Predict the number of vehicles at a peak time if the toll increases to $.00. vehicles/h Toll Traffic Volume ($) (vehicles/h) FFICE SUPPLIES The cost of paper varies directl with the number of reams of paper purchased. If reams cost $9.0, find the cost of reams. $9.0 Lesson - Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

33 - NAME DATE PERID Reading to Learn Mathematics Rate of Change Pre-Activit How are slope and speed related? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. For ever -hour increase in time, what is the change in distance? mi b. Find the slope of the line. c. Make a conjecture about the relationship between slope of the line and speed of the car. Slope is equal to the speed of the car. Reading the Lesson. See students work. Write a definition and give an eample of each new vocabular phrase. Vocabular Definition Eample. rate of change. direct variation. constant of variation Complete each sentence.. Rates of change can be described using slope.. Direct variation is a special tpe of linear equation. Helping You Remember. The word ratio comes from the Latin word meaning rate and can also mean proportion or relation. Direct variation is often called direct proportion. Look up ratio in the dictionar. Then use this information to eplain the relationship between rate of change and direct variation. Sample answers: The rate of change is the ratio of the change in one quantit to the change in another quantit. If the ratio is direct, or proportional, then both quantities var at the same, or constant, rate. Either the both increase at the same rate or the both decrease at the same rate. Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

34 - NAME DATE PERID Enrichment Fibonacci Sequence The first fifteen terms of the Fibonacci sequence are shown below.,,,,,,,,,, 9,,, 77, 0 In addition to the fact that each term is the sum of the two previous terms, there are other interesting relationships. Complete.. Find the sum of the first four terms. 7. Find the sum of the first five terms.. Find the sum of the first si terms. 0. What is the relationship between the sums and terms in the sequence? The sum is one less than the Fibonacci number after the net Fibonacci number.. Use our answer from Eercise above to predict the sum of the first 0 terms, and of the first terms. Check our answers b finding the sums., 7. Divide each of the first terms b. Make a list of the remainders. What pattern do ou see in the remainder sequence?,,,,, 0,,,,,, 0,,, ; The si digits,,,,, 0 repeat. 7. The sums of the squares of consecutive terms of the Fibonacci sequence are shown below. Complete the net three lines of this pattern. Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

35 - NAME DATE PERID Stud Guide and Intervention Slope-Intercept Form The slope-intercept form of a line makes it eas to graph the line: m b Eample: slope m slope -intercept b -intercept Eample Step Step Graph = using the slope and -intercept. Find the slope and -intercept. slope -intercept Graph the -intercept point at (0, ). Step Write the slope as. Use the slope to locate a second point on the line. m change in : down units change in : right unit Step Draw a line through the two points. Step Eercises Check b locating another point on the line and substituting the coordinates into the original equation. Given the slope and -intercept, graph each line.. slope,. slope,. slope, -intercept -intercept -intercept (0, ) (, 7) + Graph each equation using the slope and -intercept Glencoe/McGraw-Hill Glencoe Pre-Algebra

36 - NAME DATE PERID Skills Practice Slope-Intercept Form State the slope and the -intercept for the graph of each equation.... ; ; ; Lesson - Given the slope and -intercept, graph each line.. slope,. slope,. slope, -intercept -intercept -intercept + Graph each equation using the slope and -intercept Glencoe/McGraw-Hill Glencoe Pre-Algebra

37 - NAME DATE PERID Practice Slope-Intercept Form Given the slope and -intercept, graph each line.. slope,. slope,. slope, -intercept -intercept -intercept + Graph each equation using the slope and -intercept.... EXERCISE For Eercises 7 and, use the following information. A person weighing 0 pounds burns about 0 Calories per hour walking at a moderate pace. Suppose that the same person burns an average of 00 Calories per da through basic activities. The total Calories burned b that person can be represented b the equation 0 00, where represents the number of hours spent walking. 7. Graph the equation using the slope and -intercept. Calories Burned (thousands) State the slope and -intercept of the graph of the equation and describe what the represent. The -intercept 00 represents the number of Calories burned without eercising. The slope 0 represents the number of Calories burned per hour when walking Time Walking (h) Glencoe/McGraw-Hill Glencoe Pre-Algebra

38 - NAME DATE PERID Reading to Learn Mathematics Slope-Intercept Form Pre-Activit How can knowing the slope and -intercept help ou graph an equation? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. n the same coordinate plane, use ordered pairs or intercepts to graph each equation in a different color. b. Find the slope and the -intercept of each line. Complete the table. Equation Slope -Intercept Lesson - c. Compare each equation with the value of its slope and -intercept. What do ou notice? The slope is the coefficient of, the -intercept is the constant. Reading the Lesson Write a definition and give an eample of the new vocabular phrase.. Vocabular Definition Eample slope-intercept form See students work.. Sometimes ou must solve an equation for before ou can write the equation in slope-intercept form.. Eplain wh m b is called the slope-intercept form. The form m b describes a line according to its slope, m, and its -intercept, b. Helping You Remember. Mathematicians debate the origin of the slope-intercept form of a line, particularl the use of m to represent slope. Make up a mnemonic phrase to help ou remember the slope-intercept form. Sample answer: is the m(ountain slope) times plus the b(all intercepted on the -ardline). Glencoe/McGraw-Hill Glencoe Pre-Algebra

39 NAME DATE PERID - Enrichment Translations and Reflections The lines on graph paper can help ou draw slide images of figures.. Graph ABC with vertices A(, ), B(, ), and C(, ). Draw A B C, the translation image of ABC, where the slide is units to the right. Name the coordinates of the image of each verte. A (, ), B (0, ), C (0, ). Draw JKL with vertices J(, ), K(0, ), and L(, 0). Let J K L be the image of JKL under a slide of units to the right and then a slide of units up. Graph J K L. Name the coordinates of the vertices of J K L. J (0, ), K (, ), L (, ). Draw A B, the image formed b reflecting A B over the -ais. Then draw A B, the image formed b reflecting A B over the -ais. What are the coordinates of A and B? What is the relationship between the coordinates of the endpoints of A B and those of A B? B. Draw P Q, the reflection image of P Q over the -ais. Draw P Q, the reflection image of P Q over the -ais. Find the slopes of P Q, P Q, and P Q. What is the relationship between the slopes of P Q and P Q? Q Q A P P P Q A (, ), B (, ); The coordinates of A and B have the opposite signs of A and B. Slope of P Q ; slope of P Q ; slope of P Q ; The are the same. Glencoe/McGraw-Hill Glencoe Pre-Algebra

40 -7 NAME DATE PERID Stud Guide and Intervention Writing Linear Functions If ou know the slope and -intercept, ou can write the equation of a line b substituting these values in m b. Eample Write an equation in slope-intercept form for each line. a. slope, -intercept b. slope 0, -intercept 9 m b Slope-intercept form m b Slope-intercept form ( ) Replace m with and b with. 0 ( 9) Replace m with 0 and b with 9. Simplif. 9 Simplif. Lesson -7 Eample Write an equation in slope-intercept form for the line passing through (, ) and (, 7). Step Find the slope m. m Definition of slope 7 m or ( ) (, ) (, ), (, ) (, 7) Step Find the -intercept b. Use the slope and the coordinates of either point. m b Slope-intercept form Eercises ( ) b Replace (, ) with (, ) and m with. b Simplif. An equation is. Write an equation in slope-intercept form for each line.. slope,. slope,. slope 0, -intercept -intercept -intercept Write an equation in slope-intercept form for the line passing through each pair of points.. (, ) and (, ). (, ) and (, ). (7, ) and (, ) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

41 -7 NAME DATE PERID Skills Practice Writing Linear Functions Write an equation in slope-intercept form for each line.. slope 7,. slope,. slope, -intercept -intercept -intercept 7. slope,. slope 7,. slope, -intercept 7 -intercept -intercept Write an equation in slope-intercept form for the line passing through each pair of points.. (9, ) and (, ). (, ) and (, ). (0, ) and (, ). (, ) and (, ) 7. (, ) and (, 9). (, ) and (, ) 9. (, 0) and (, ) 0. (, ) and (, ). (, 0) and (, ) Glencoe/McGraw-Hill Glencoe Pre-Algebra

42 -7 NAME DATE PERID Practice Writing Linear Functions Write an equation in slope-intercept form for each line.. slope,. slope 0, -intercept -intercept Lesson -7 Write an equation in slope-intercept form for the line passing through each pair of points.. (9, 0) and (, ). (, ) and (, ) 7. (7, ) and (, ). (, 7) and (, ) 9. (, ) and (, 0) 0. (0, ) and (, ) BUSINESS For Eercises and, use the following information. Flourishing Flowers charges $ plus $0 for each standard floral arrangement to deliver and set up flowers for a banquet.. Write an equation in slope-intercept form that shows the cost for flowers for number of arrangements. 0. Find the cost of providing 0 floral arrangements. $ INSULATIN For Eercises and, use the following information. Renata González wants to increase the energ efficienc of her house b adding to the insulation previousl installed. The better a material protects against heat loss, the higher its R-value, or resistance to heat flow. The table shows the R-value of fiberglass blanket insulation per inch of thickness. The eisting insulation in Renata s attic has an R-value of 0.. Write an equation in slope-intercept form that shows the total R-value in the attic if she adds number of inches of additional insulation.. 0 R-value. Estimate the total R-value in the attic if she adds inches of insulation. 9. Thickness (in.) Source: ak Ridge National Laborator Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

43 -7 NAME DATE PERID Reading to Learn Mathematics Writing Linear Functions Pre-Activit How can ou model data with a linear equation? Do the activit at the top of page 0 in our tetbook. Write our answers below. a. Graph the ordered pairs (chirps, temperature). Draw a line through the points. Temperature ( F) Reading the Lesson Number of Chirps b. Find the slope and the -intercept of the line. What do these values represent? Slope represents the rate of change, degree for ever chirp; -intercept 0 represents the temperature at which the crickets are not chirping. c. Write an equation in the form m b for the line then translate the equation into a sentence. 0; The temperature equals the number of chirps in seconds plus 0.. Eplain how ou can use the following information to write the slope-intercept form of a line. a. graph of a line Find the -intercept. From that point, count how man units up or down and how man units left or right to another point. The slope is the ratio of the rise over the run. Then substitute the slope and the -intercept into the slope-intercept form. b. two points on a line Substitute the coordinates of two points on the line into the definition of slope. Then use the slope and one of the points to find the -intercept. Substitute the slope and the point s coordinates into slope-intercept form. Then substitute the slope and the -intercept into the slope-intercept form. c. a table of values Use the table to identif the coordinates of two points on the line. Then substitute the coordinates of the two points on the line into the definition of slope. Then use the slope and one of the points to find the -intercept. Substitute the slope and the point s coordinates into slope-intercept form. Then substitute the slope and the -intercept into the slope-intercept form. Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

44 -7 NAME DATE PERID Enrichment Problem Solving: Gathering Data When investors decide to bu or sell stock, the usuall base their decisions on data. The read stock market reports, investigate companies the are interested in, and look at economic trends. This activit focuses on reading stock market reports. To read a stock market report, ou need to become familiar with the terms that are used, the facts and figures that are published in the newspaper, and the methods used to keep track of the stocks. Man newspapers print stock reports such as the New York Stock Echange (NYSE) report. The final entr for each stock is a fraction or mied number that is positive (indicating a gain in value) or negative (indicating a loss). Find the New York Stock Echange (NYSE) report in the business section of our local Sunda newspaper. Using just those stocks that begin with A, B, or C, tall the number of stocks that had each of the gains and losses listed below. Lesson -7 points or more No change points or more. Answers will var.. Did more stocks gain in value or lose value?. How did the market do as a whole?. How did the newspapers describe the trading this week?. Make a scatterplot that shows how two specific stocks change over the period of one week. Use their dail closing prices.. Is there an relationship between the two stocks ou chose? Eplain wh or wh not. Glencoe/McGraw-Hill Glencoe Pre-Algebra

45 - NAME DATE PERID Stud Guide and Intervention Best-Fit Lines A best-fit line is a line that is ver close to most of the data points. You can use best-fit lines to make predictions from real-world data. Eample Make a scatter plot and draw a best-fit line for the data in the table. Year Percent of Population Source: U.S. Census Bureau Year Percent of Population Percent of Population U.S. Civilian Labor Force Year Source: U.S. Census Bureau Eample Eercises Use the best-fit line in eample to predict the percent of the population in the U.S. labor force in 00. Use the etended line to find the value for an value of 00 about 70. A prediction for the percent of the U.S. population in the labor force in 00 is approimatel 70 percent. Use the table that shows the number of girls who participated in high school athletic programs in the United States from 97 to 99.. Make a scatter plot and draw a best-fit line. Number of Participants (thousands) Year Year Number of Participants (thousands) Source: U.S. Census Bureau Use the best-fit line to predict the number of female participants in 00. Sample answer: about,000,000 female participants Glencoe/McGraw-Hill Glencoe Pre-Algebra

46 - NAME DATE PERID Skills Practice Best-Fit Lines CNSTRUCTIN For Eercises and, use the table that shows the average hourl wage of U.S. construction workers from 90 to Make a scatter plot and draw a best-fit line. Average Hourl Wage ($) Year Average Hourl Earnings ($) Source: U.S. Census Bureau. Use the best-fit line to predict the average hourl wage of construction workers in 00. Sample answer: about $ MINING For Eercises and, use the table that shows the number of persons emploed in mining from 90 to Make a scatter plot and draw a best-fit line. Emploees (thousands) Year Source: U.S. Census Bureau Year Emploees (thousands) Source: U.S. Census Bureau Lesson -. Write an equation for the best-fit line and use it to predict the number of persons emploed in mining in 00. Sample answer:,07; approimatel 7,000 emploed persons Glencoe/McGraw-Hill Glencoe Pre-Algebra

47 - NAME DATE PERID Practice Best-Fit Lines BEVERAGES For Eercises and, use the table that shows the amount of whole milk consumed per person in the United States from 99 to Make a scatter plot and draw a best-fit line. Gallons per Person Year Gallons per Person Source: U.S. Census Bureau. Use the best-fit line to predict the amount of whole milk consumed per person in 00. Sample answer: about gallons of whole milk per person EDUCATIN For Eercises and, use the table that shows the number of students graduating from medical school in the United States from 90 to Make a scatter plot and draw a best-fit line. Number of Graduates,000 7,00 7,000,00,000,00,000, Year Source: U.S. Census Bureau Year Graduates 90, 9, 990,9 99, 000, Source: U.S. Census Bureau. Write an equation for the best-fit line and use it to predict the number of medical school graduates in 00. Sample answer:. 7,; approimatel,0 medical school graduates Glencoe/McGraw-Hill Glencoe Pre-Algebra

48 - NAME DATE PERID Reading to Learn Mathematics Best-Fit Lines Pre-Activit How can a line be used to predict life epectanc for future generations? Do the activit at the top of page 09 in our tetbook. Write our answers below. a. Use the line drawn through the points to predict the life epectanc of a person born in 00. b. What are some limitations in using a line to predict life epectanc? Sample answer: Medical improvements could change the accurac of the model. Also, the line continues to go up, but people s ages will not increase forever. Reading the Lesson Write a definition and give an eample of the new vocabular phrase. Vocabular Definition Eample. slope intercept form See students work. Lesson -. A best-fit line can be used when the data points approimate a linear relationship.. Eplain what a prediction equation is. A prediction equation is an equation of a best-fit line used to tell what course the data will likel take in the future. Helping You Remember. Complete the following concept map showing the steps needed to find a prediction equation and make a prediction. Step Select on the line. Find the. Step Find the. Write the in. Step Write the equation of the. Replace in the equation with the - value of a on the line. to find. Glencoe/McGraw-Hill Glencoe Pre-Algebra

49 - NAME DATE PERID Enrichment Line of Best Fit Each point on the graph shows the relation between the number of people attending the Ro Cinema and the number of cars in the parking lot. A line is drawn that appears to lie close to most of the points. This is called the line of best fit. Here is how to find the equation of this line. The line passes through (00, 0) and (00, 0). Use the slope intercept form. Number of Cars Attendance and Parking Cinema Attendance m Definition of slope m b Slope-intercept form 0 0 m (, ) (00,0) (, ) (00,0) 0 (00) b Replace (, ) with (00, 0) and m with. 0 or Simplif. 0 b Simplif. 00 So an equation for the line is 0or. Solve each problem.. Suppose the owner of the Ro decides to increase the seating capacit of the theater to 000. How man cars should the parking lot be prepared to accommodate? 00 cars. The points (0, 0) and (0, 0) lie on the scatter plot. Write an equation for the line through these points.. Do ou think the equation in Eercise is a good representation of the relationship in this problem? Eplain. No; The graph of the equation does not appear to go through the center of the data points.. Suppose the equation for the relationship between attendance at the theater and cars in the parking lot is 0. What might ou suspect about the users of the parking lot? Man people are parking in the lot who are not going to the Ro. Glencoe/McGraw-Hill Glencoe Pre-Algebra

50 -9 NAME DATE PERID Stud Guide and Intervention Solving Sstems of Equations Two linear equations together are called a sstem of equations. ne method for solving a sstem of equations is to graph the equations on the same coordinate plane. Another wa to solve a sstem of equations is b using substitution. Eample Solve the sstem of equations b graphing. The graphs appear to intersect at (, ). Check this estimate b substituting the coordinates into each equation. CHECK: () (, ) Eample Eercises Solve the sstem of equations b substitution. Since must have the same value in both equations, ou can replace with in the first equation. Write the first equation. Replace with. Solve for. The solution of this sstem of equations is (, ). Check b graphing. Solve each sstem of equations b graphing... (, 0) (, 0) (, ) (, ) Lesson -9 Solve each sstem of equations b substitution (, ) (, ) (, ) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

51 -9 NAME DATE PERID Skills Practice Solving Sstems of Equations Solve each sstem of equations b graphing.... (, ) (0, ) (, ) no solution (0, )... (, ) (, 0) (, ) infinitel man (, 0) Solve each sstem of equations b substitution (, ) (, ) (, ) , (, ) (, ) Glencoe/McGraw-Hill Glencoe Pre-Algebra

52 -9 NAME DATE PERID Practice Solving Sstems of Equations Solve each sstem of equations b graphing (, ) (, 0) infinitel man (, ) (, 0) Solve each sstem of equations b substitution.... (, 7) (, ) (, ) (0, ) (, ) (, ) SHPPING For Eercises 0, use the following information and the table. At-Home Dr Cleaning Lesson -9 Brand Price per Kit Price per Refill A $.00 $.00 B $9.00 $0.0 Two brands of at-home dr cleaning products sell both start-up kits and refill packets. Each start-up kit does five loads of dr cleaning. Each refill does one load. 0. Write a sstem of equations that represents the cost for number of loads. and Solve the sstem of equations. Eplain what the solution means. (, 0); The cost of a kit and refills is the same for both brands.. If ou do nine loads of dr cleaning, which brand would be less epensive? Eplain. Brand B; $ $ Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

53 -9 NAME DATE PERID Reading to Learn Mathematics Solving Sstems of Equations Pre-Activit Reading the Lesson How can a sstem of equations be used to compare data? Do the activit at the top of page in our tetbook. Write our answers below. a. Write an equation to represent the income from each job. Let equal the salar and let equal the number of hours worked. (Hint: Income hourl rate number of hours worked bonus.) 0 0 and b. Graph both equations on the same coordinate plane. c. What are the coordinates of the point where the two lines meet? What does this point represent? (0, 0); In 0 hours, the salar will be the same for both jobs, $0.. See students work. Write a definition and give an eample of each new vocabular word or phrase. Vocabular Definition Eample. sstem of equations. substitution. The solution of a sstem of equations is the coordinates of the point where the graphs of the equations intersect.. If two equations have the same graph, there are infinitel man solutions to that sstem of equations. Helping You Remember. Review the Stud Tip on page in our tetbook. Complete each section of the chart with the number of solutions and an eplanation, model, or logical proof for the situation. Sample answers are given. Salar ($) Number of Hours Different Slopes Eactl one solution; if two lines have different slopes, the will meet at one point even if that point is far beond the scope of the graph. Because both lines are straight, the will onl meet once. Same Slope, Different -Intercepts No solution; if two lines have the same slope but different -intercepts, the are parallel lines. B definition, the two lines will never meet Same Slope, Same -Intercept Infinitel man solutions; if two lines have the same slope and the same -intercept, then the have the same graph. An point on the graph satisfies both equations. Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

54 -9 NAME DATE PERID Enrichment Graphing Sstems of Equations Because checking accounts var from one financial institution to another, educated consumers should carefull weigh the options offered b various institutions when choosing a checking account. The four equations below describe the cost of four different checking accounts. In each equation, C represents the monthl cost in dollars, and n represents the number of checks written. Find the cost for the number of checks written in each account. Account Account Account Account C 0.n.0 C 0.n.00 C 0.n 0.7 C 0.0n.7 n C n C n C n C 0 $.0 $.70 $.00 $.0 $.70 $.00 0 $.00 $.0 $.0 $.00 $.0 0 $.00 0 $0.7 $.0 $.00 $. $.7 9 $.00 0 $.7 $. $.00 9 $.0 $. 0 $.7 Graph and label each account on the grid. Cost in Dollars C Lesson Number of Checks N. The break-even point of the graph is the point at which the costs of the accounts are the same. What is the break-even point for these accounts? five checks, a cost of $.00. Which account should be chosen b a consumer who writes fewer than five checks per month? Account. Which account should be chosen b a consumer who writes more than five checks per month? Account Glencoe/McGraw-Hill Glencoe Pre-Algebra

55 -0 NAME DATE PERID Stud Guide and Intervention Graphing Inequalities To graph a linear inequalit, first graph the boundar. Test an point to determine which region is the solution, or half plane. Shade this region. You can also use inequalities to solve real-world problems. Eample GARDENING Marisol has 0 square feet in her garden for planting squash and peppers. How man square feet can she plant of each? Squash plus peppers is at most 0 square feet Eercises Write the inequalit. Subtract from each side. Graph 0 as a solid line since the boundar is part of the graph. The origin is part of the graph since Thus, the coordinates of all points in the shaded region are possible solutions. (7, ) 7 square feet of squash, square feet of peppers (, ) square feet of squash, square feet of peppers (, 7) square feet of squash, 7 square feet of peppers Peppers (sq ft) Squash (sq ft) LEISURE Use the following information for Eercises. Fred and Roa have $00 to spend on ballroom dancing classes. Each fotrot class costs $ per couple and each salsa lesson costs $0 per couple.. Write an inequalit to represent this situation Graph the inequalit. Salsa Classes Fotrot Classes. Use the graph to determine how man of each tpe of dance class Fred and Roa can take. Sample answers: ( fotrot, salsa) (0 fotrot, 7 salsa), ( fotrot, 0 salsa) Glencoe/McGraw-Hill Glencoe Pre-Algebra

56 -0 NAME DATE PERID Skills Practice Graphing Inequalities Graph each inequalit PACKING For Eercises 7 9, use the following information. The Gelbs are moving to a new home and want to pack efficientl. The boes the are using can hold 0 pounds each. Suppose that each book weighs pound and ever sweater weighs pounds. Assume that the boes are large enough to hold an combination of books and sweaters weighing 0 pounds or less. 7. Write an inequalit to represent this situation. 0. Graph the inequalit. Sweaters (lb) 9 7 Lesson Books (lb) 9. Use the graph to determine how man books and how man sweaters each bo can hold. Sample answers: ( books, sweaters), (0 books, 0 sweaters), ( books, sweaters) Glencoe/McGraw-Hill Glencoe Pre-Algebra

57 -0 NAME DATE PERID Practice Graphing Inequalities Graph each inequalit.... DRIVING For Eercises, use the following information. Sarah needs to spend at least 90 hours driving in order to qualif to take a driver s test. She can either drive with a licensed instructor or her parent or guardian.. Write an inequalit to represent this situation. 90. Graph the inequalit.. Use the graph to determine how man hours Sarah can drive with an instructor or a parent. Sample answers: (0 instructor, 90 parent), (0 instructor, 0 parent), (0 instructor, 90 parent) READING For Eercises 7 9, use the following information. Parent (h) Instructor (h) Jai joined a reading club for the summer. He pledged to read more than 00 points worth of reading material. Books count 0 points each while other materials such as magazines, poems, or short stories count points each. 7. Write an inequalit to represent this situation Graph the inequalit. 9. Use the graph to determine how man books and how man pieces of other material Jai needs to read to meet his commitment. Sample answers: (0 books, 0 other), (0 books, 70 other), (0 books, 0 other) ther Materials Books Glencoe/McGraw-Hill Glencoe Pre-Algebra

58 -0 NAME DATE PERID Reading to Learn Mathematics Graphing Inequalities Pre-Activit How can shaded regions on a graph model inequalities? Do the activit at the top of page 9 in our tetbook. Write our answers below. a. Substitute (, ) and (, ) in. Which ordered pair makes the inequalit true? (, ) b. Substitute (, ) and (, ) in. Which ordered pair makes the inequalit true? (, ) c. Which area represents the solution of? shaded area Reading the Lesson. See students work. Write a definition and give an eample of each new vocabular word or phrase. Vocabular Definition Eample. boundar. half plane. If an inequalit contains or, then use a solid line to indicate that the boundar is included in the graph.. If an inequalit contains or, then use a dashed line to indicate that the boundar is not included in the graph. Helping You Remember. Suppose that for the net seven das, ou can have either an apple or an orange with our lunch. Graph all possible solutions on a coordinate grid. Assume that each da ou have eactl one whole fruit. Then suppose that ou have a total of. apples and. Apples oranges during the seven das. Plot this solution point on the grid and shade the region containing this point. What advantages does graphing the inequalit have over graphing just the points? Graphing the inequalit makes it possible to show a more comple situation, including the possibilit of having part of a fruit or no fruit at all on some das. ranges Lesson -0 Glencoe/McGraw-Hill Glencoe Pre-Algebra

59 -0 NAME DATE PERID Enrichment Graphing Sstems of Inequalities Suppose ou are given the following sstem of inequalities. The solution of this sstem is the set of all ordered pairs that satisf both inequalities. To find the solution, graph each inequalit. The intersection of the graphs represents the solution. The graphs of the equations and are the boundaries of each region. The solution of the sstem is the region that contains ordered pairs that are solution of both inequalities. For eample, (, ) is a solution of the sstem. Check b substituting the coordinates into each inequalit. Solve each sstem b graphing. State one solution of each sstem.. Sample solutions are given.... (, ) (, ) (0, )... (, ) (, ) (, ) Glencoe/McGraw-Hill Glencoe Pre-Algebra

60 NAME DATE PERID Chapter Test, Form SCRE Write the letter for the correct answer in the blank at the right of each question.. Determine which relation is a function. A. {(, 0), (0, ), (, ), (0,)} B. {(0, 0), (0, ), (0, ), (0,)} C. {(, 0), (0, ), (, ), (, )} D. {(, 0), (, ), (, ), (, )}.. The relation {(, 0), (, 9), (, )} is not a function when which ordered pair is added to the set? A. (, 0) B. (9, ) C. (, ) D. (, 7).. The table shows the projected ratio of males to females at various ages in the ear 0. Determine whether this relation is a function and describe the relationship between the age of the population and the ratio of males to females. Age 7 Ratio Source: A. Function; as the age increases, the ratio increases. B. Function; as the age increases, the ratio decreases. C. Not a function; as the age increases, the ratio increases. D. Not a function; as the age increases, the ratio decreases... Which of the following is not a solution of the equation? A. (, ) B. (, ) C. (0, ) D. (, ).. Which set of ordered pairs can be used to graph. A. (, ), (, ), (, ) B. (, ), (, ), (, ) C. (, ), (, ), (, ) D. (, ), (, ), (, ).. Find the -intercept and the -intercept for the graph of. A. ; B. ; C. ; D. ;. 7. Draw a graph of the equation with intercepts (0, ) and (, 0) to determine which other point the line passes through. A. (, ) B. (, ) C. (, ) D. (, ) 7.. Find the slope of the line that passes through the points A(0, ) and B(, 0). A. B. C. D.. 9. The slope of a horizontal line is?. A. undefined B. 0 C. positive D. negative Suppose varies directl with and when. Write an equation relating and. A. B. C. D. 0. Assessment Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

61 NAME DATE PERID Chapter Test, Form (continued). The table shows the temperature of a potato placed in a 00 oven. What is the rate of change of temperature of the potato in the first 0 minutes? t (minutes) T (temperature) A. 0 B. C. per minute D. per minute. 7. State the slope and the -intercept for the graph of. A. ; none B. ; C. ; D. ; 0.. Write an equation in slope-intercept form to represent the table of values. 7 A. B. C. D... The graph of a line goes through the point at (0, ) and has slope. Which point is also on the graph of the line? A. (, ) B. (, ) C. (, ) D. (, ). For Questions and, the scatter plot at the right shows the relationship between the age and value of a used car in each of four ears.. Which of the following is the best estimate for the slope of the best-fit line for the data? A. 000 B. C. D. 0.. Use a best-fit line to predict the value of the car after five ears. A. $,700 B. $,00 C. $,00 D. $0, Find the solution of the sstem of equations graphed. A. (, ) B. (0, ) and (, 0) C. (, ) D. (0, ) and (, 0) 7.. Solve the sstem of equations at the right b substitution. 0 A. (, ) B. (0, ) C., D. (, 0). 9. The graph of is the region? the graph of. A. below B. above C. on or below D. on or above Determine which ordered pair is a solution of the inequalit 7. A. (, ) B. (0, ) C. (, ) D. (, 0) 0. Bonus The price of buing gasoline varies directl with the B: number of gallons bought. If five gallons of gas cost $7.0, what is the rate of change of this linear function? Glencoe/McGraw-Hill Glencoe Pre-Algebra Value (hundreds of dollars) 0 0 Age (ears)

62 NAME DATE PERID Chapter Test, Form A SCRE Write the letter for the correct answer in the blank at the right of each question.. Determine which relation is not a function. A. {(, ), (, ), (, ), (, )} B. {(0, ), (, ), (, ), (0, )} C. {(., ), (, ), (, ), (, )} D. {(, ), (0., ), (, ), (, )}.. Which of the following values of c makes the relation {(0, ), (, ), (, ), (c,)} a function? A. B. C. 0 D. None of these.. The table shows the median ears that workers of various ages had worked for their current emploer. Determine whether this relation is a function, and describe the relationship between age and length of time with the current emploer. Source: Age Years with Emploer A. Function; as the worker gets older, the median ears of work increases. B. Function; as the worker gets older, the median ears of work decreases. C. Not a function; as the worker gets older, the median ears of work increases. D. Not a function; as the worker gets older, the median ears of work decreases... Which of the following is a solution of? A. (, ) B. (0, ) C. (, 0) D. (, ).. Which set of ordered pairs can be used to graph? A. (, ), (0, ), (, 0) B. (, ), (0, ), (, 0) C. (, ), (0, 0), (, ) D. (, ), (0, ), (, 0).. Find the -intercept and the -intercept of the graph of. A. ; B. ; C. ; D. ;. 7. Draw a graph of the equation with intercepts (0, ) and (, 0) to determine which other point the line passes through. A. (, ) B. (, ) C. (, ) D. (, ) 7.. Find the slope of the line that passes through the points A(, ) and B(, ). A. B. C. D.. 9. What is the slope of the line? A. B. 0 C. undefined D In 99, the number of visitors to water parks was. million, while in 999, the number of visitors dropped to.7 million. What was the rate of change? Source: Amusement Business A. 00 B. 7.% decrease C. 0. million people D., fewer people per ear 0. Assessment Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

63 NAME DATE PERID Chapter Test, Form A (continued). The number of ards varies directl as the number of feet. Write an equation converting feet to ards, using the fact that there are three feet in a ard. A. B. C. D... Find the slope and the -intercept for the graph of. A. ; none B. ; C. 0; D. ; 0.. Write an equation in slope-intercept form to represent the table of values. 9 9 A. B. C. D... The graph of a line goes through the point at (0, ) and has slope.which point is also on the graph of the line? A. (, ) B. (, ) C. (, ) D. (, ). For Questions and, the scatter plot at the right shows the relationship between Drop vs Speed 0 height of the hill and speed of a roller coaster.. Which of the following could be the slope of the best-fit line for the data? A. B. C. 0 D Speed (mph). Predict the height of a hill for a roller coaster that has a speed of 90 mph. A. 0 ft B. 70 ft C. 0 ft D. 0 ft. 7. Solve the sstem of equations 0 at the right b graphing. 0. A. (0, 0) B. no solution C. infinitel man solutions D. ( 0., ) 7.. Solve the sstem of equations at the right b substitution. A. (, ) B. (0, ) C., D. (, 0). 9. The graph of is the region? the line. A. below B. above C. on or below D. on or above Determine which ordered pair is not a solution of the inequalit. A. (, ) B. (0, ) C. (, 7) D. (, 0) 0. Bonus In a certain linear equation, the rate of change of with B: respect to is two. Write the equation if the (0, ) is a solution. Glencoe/McGraw-Hill 70 Glencoe Pre-Algebra Drop (feet)

64 NAME DATE PERID Chapter Test, Form B SCRE Write the letter for the correct answer in the blank at the right of each question.. Determine which relation is not a function. A. {(, ), (, ), (, ), (, )} B. {(0, ), (, ), (, ), (, )} C. {(, ), (, ), (, ), (, )} D. {(, ), (, ), (, ), (, )}.. Which of the following values of d makes the relation {(, 0), (, ), (, ), (d, )} a function? A. B. C. D. None of these.. The table shows the percent of households of a given income that have computers. Determine whether this relation is a function, and describe the relationship between the household income and the percent of those households that have computers. Source: Household Income ($),00,00 0,000,00,00 7,000 Percent with Computer A. Function; as income rises, the number of computers in each household increases. B. Function; as income rises, the percent of homes with computers increases. C. Not a function; as income rises, the number of computers in each household increases. D. Not a function; as income rises, the percent of homes with computers increases... Which of the following is not a solution of? A. (, ) B. (0, ) C. (, ) D. (, ).. Which set of ordered pairs can be used to graph? A. (, 9), (, ), (, 9) B. (, ), (, ), (, 9) C. (, ), (0, ), (, ) D. (, 9), (, ), (, 9).. Find the -intercept and the -intercept of the graph of. A. ; B. ; C. ; D. ;. 7. Draw a graph of the equation with intercepts (, 0) and (0, ) to determine which other point the line passes through. A. (, ) B. (, ) C. (, ) D. (, ) 7.. Find the slope of the line that passes through the points A(, ) and B(, ). A. B. C. D. 9. What is the slope of the line? A. B. 0 C. undefined D College tuition and fees in the ear 000 averaged $0 a ear at fourear public institutions compared to $7 in 99. What was the rate of change? A. $9 B. $.0 per ear C. $.0 D. 9.% 0. Assessment Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

65 NAME DATE PERID Chapter Test, Form B (continued). The number of feet varies directl as the number of inches. Write a direct variation equation that converts inches to feet, using the fact that there are twelve inches in a foot. A. B. C. D... State the slope and the -intercept for the graph of. A. 0; B. undefined; C. ; 0 D. 0; 0.. Write an equation in slope-intercept form to represent the table of values. 9 7 A. B. C. D... The graph of a line goes through (0, ) and has slope. What point is also on the graph of the line? A. (, ) B. (, ) C. (, ) D. (, ). For Questions and, the scatter plot at the Percent of US Cities right shows the relationship between the ear with Youth Curfews and the percent of cities having outh curfews.. Which of the following could be the slope of the best-fit line for the data? A. 7 B. 7 C. 70 D Predict the percent of cities having outh curfews in 999. A. 9 B. C. 70 D. 0 Year. 7. Solve the sstem of equations 0 at the right b graphing. A. (0, 0) and (, ) B. no solution ''7'9'9'9'9'97'99 C. infinitel man solutions D. ( 0., ) 7.. Solve the sstem of equations at the right b substitution. A., B. (, ) C. (, ) D. no solutions. 9. The graph of is the region? the graph of. A. on and above B. on and below C. above D. below Determine which ordered pair is a solution of the inequalit. A. (0, ) B. (, ) C. (, ) D. (, ) 0. Bonus In a certain linear equation, the rate of change of with B: respect to is. Write the equation if (0, ) is a solution of the equation. Percent of Cities Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

66 NAME DATE PERID Chapter Test, Form C SCRE For Questions and, determine whether each relation is a function.. {(, 0), (0, 0), (, 0), (, )}.... The table shows the percent of people in the U.S. that are. enrolled in post-secondar education for various ages. Is this relation a function? Describe the relationship between age and the percent of people enrolled in higher education. Source: Age Percent Enrolled 9. Find four solutions of. Write the solutions as. ordered pairs.. Graph b plotting ordered pairs... Find the -intercept and the -intercept for the graph of Graph using the - and - intercepts. 7.. Use the graph at the right. Find the slope of the line.. 9. Find the slope of the line that passes through the points 9. A(, ) and B(, ). 0. The table shows the percent of adults who used computers 0. from What is the rate of change from 9 to 99? Source: Year Percent of Adults. State the slope and the -intercept of the graph of.. Assessment Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

67 NAME DATE PERID Chapter Test, Form C (continued). The number of kilometers in a measure varies directl as. the number of miles. Write a direct variation equation that could be used to convert miles to kilometers, if miles is about.0 kilometers.. State the slope and the -intercept of a graph that. represents the linear data in the table Graph a line with slope and -intercept.. For Questions and, use the. 00 scatter plot at the right that shows SAT scores and overall 00 math grades. 00. Draw a best-fit line for the data. SAT Scores 00 SAT Scores Math Grade Math Grade. Predict the SAT score of a student whose overall math. grade is. 7. Solve the sstem of equations at the right b graphing. 7.. Solve the sstem of equations 7. at the right b substitution. 9. Graph Punch is to be made using orange juice and ginger-ale. Write an inequalit showing how man gallons of each could be used if the punch is made in a ten-gallon container. 0. Bonus Water is being pumped out of a pool. The number of B: gallons of water W left in the pool at time t in minutes can be modeled b W(t) 7t 0. Find the -intercept and eplain what it represents in this problem. Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

68 NAME DATE PERID Chapter Test, Form D SCRE For Questions and, determine whether each relation is a function.. {(, ), (0, ), (, ),.. (, ), (, ), (, )}.. The table shows the average commuting time for workers. in cities. Is this relation a function? Describe the relationship between the working population and the average time spent commuting. Source: Number of Workers (hundred thousands) Time of Commute (minutes) Find four solutions of. Write the solutions as. ordered pairs.. Graph b plotting ordered pairs... Find the -intercept and the -intercept of the graph of.. 7. Graph using the - and -intercepts. 7.. Use the graph at the right. Find the slope of the line. 9. Find the slope of the line that. passes through the points A(, ) and B(, ) The table shows the percent of adults who used computers 0. from 9 through 99. What was the rate of change from 99 to 99? Source: Year Percent of Adults. State the slope and the -intercept of the graph of.. Assessment Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

69 NAME DATE PERID Chapter Test, Form D (continued). The number of miles in a measure varies directl as the. number of kilometers. Write a direct variation equation that could be used to convert kilometers to miles, if kilometers is about.07 miles.. State the slope and the -intercept of a graph that. represents the linear data in the table. 7. Graph a line with slope and -intercept.. For Questions and, use the. scatter plot at the right that shows the relationship between the blood pressure and ages of different people.. Draw a best-fit line for the data Blood Pressure Age Blood Pressure Age. Predict the blood pressure of a 0-ear old.. 7. Solve the sstem of equations at the right b graphing. 7.. Solve the sstem of equations. at the right b substitution. 9. Graph Garden soil is made b miing sand and peat moss. Sand costs $ per pound and peat moss costs $ per pound. Write an inequalit showing how man pounds of each could be purchased for a maimum of $0. 0. Bonus The profits P in dollars from a lemonade stand can be B: modeled b the equation P() 0..0, where represents the number of glasses sold. Find the -intercept and eplain what it represents in this problem. Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

70 NAME DATE PERID Chapter Test, Form SCRE For Questions and, determine whether each relation is a function.. {(, ), (0, ), (, ), (, ), (, ), (, )}.... The table shows a relationship between and. Is this. relation a function? Describe the relationship between and Find four solutions of. Write the solutions as. ordered pairs.. Graph 9 b plotting ordered pairs... The equation 9 0 is used to convert degrees. 9 Fahrenheit to degrees Celsius. Name the -intercept of this line and describe what it means. 7. Graph using the - and -intercepts. 7.. Find the slope of the line.. 9. Find the value of b so that the slope of the line passing 9. through the points A(, ) and B(, b) is. 0. The table shows the percent of children aged to 7 who 0. used computers at school from 9 through 99. What was the rate of change from 99 to 99? Source: Year Percent. State the slope and the -intercept of the graph of.. Assessment Glencoe/McGraw-Hill 77 Glencoe Pre-Algebra

71 NAME DATE PERID Chapter Test, Form (continued). The number of quarts in a measure varies directl as the. number of liters. Write a direct variation equation that could be used to convert liters to quarts, if liters is about.. quarts.. Graph a line with slope. and -intercept.. Use the table of values to write an equation in slope-intercept form. 0 For Questions and, use the scatter plot at the right that shows the relationship between the temperature rating and the cost of different sleeping bags.. Draw the best-fit line for the data and find the rate of change. Cost (dollars) Temperature Rating ( F) Cost (dollars) Temperature Rating ( F). Predict the cost of a sleeping bag rated to Estimate the solution of the sstem of equations b graphing. and. Solve the sstem of equations b substitution. 0 and Louis makes $0 for each ard he mows and $0 for each lawn he weeds. He wants to make at least. $0 each week. 9. Write an inequalit to represent this situation State one possible solution in which he earns $0 and one 0. in which he earns more than $0. Bonus Fine Fone charges a monthl fee of $0 plus $0.0 for B: ever minute called. Cell Service charges $ each month plus $0.0 per minute. How man minutes must be called for the monthl bill to be the same for these competitors? What will be the monthl bill? 7. Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

72 NAME DATE PERID Chapter pen-ended Assessment SCRE Demonstrate our knowledge b giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justif our answers. You ma show our solution in more than one wa or investigate beond the requirements of the problems.. A corporation has a goal of increasing sales b $00,000 each ear. Sales for the first ear were $9,000. Write an equation in slope-intercept form that describes this situation. What is the meaning of the slope and -intercept of our equation?. A second goal of this corporation is to limit the increase in epenses each ear to less than $,000. Epenses the first ear were $,000. Write an inequalit that describes this situation. What is the goal for epenses in the th ear?. The fee for renting a VCR for a business meeting is given b, where is the number of hours rented and is the total rental fee in dollars. a. Find three solutions of the equation and draw the graph. b. Choose the number of hours for a rental and use the graph to determine the rental fee. Eplain each step. c. Find the -intercept and eplain what it represents. d. Do negative values of make sense? Wh or wh not?. Another compan also provides VCR rentals. Their rental equation is. a. Graph the equation using the - and -intercepts. b. Compare and contrast this graph with the graph in Question. Use the words slope and intercept in our answer. c. From which compan would ou rent a VCR? Eplain our reasoning.. The home office of a compan has limited the number of sales associates and clerical people in a branch office to 7 or fewer. a. If is the number of sales associates and is the number of clerical people, write and graph an inequalit for this situation. b. Does (, ) satisf the inequalit? What does (, ) represent? c. Name an ordered pair that does not satisf the inequalit. What does our ordered pair represent? Assessment Glencoe/McGraw-Hill 79 Glencoe Pre-Algebra

73 NAME DATE PERID Chapter Vocabular Test/Review SCRE best-fit line boundar constant of variation direct variation function half plane linear equation rate of change slope slope-intercept form substitution sstem of equations vertical line test -intercept -intercept Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.. In a relation, for each element of the domain, there is onl. one corresponding element in the range.. A linear equation in two variables is an equation in which. the variables appear in separate terms, and neither variable contains an eponent other than.. A(n) -intercept is the -coordinate of a point where a graph. crosses the -ais.. Slope describes the steepness of a line... The constant of variation is a special tpe of linear equation. that describes rate of change.. In the equation k, k is the direct variation.. 7. The equation m b is the constant of variation. 7.. A best-fit line can be used to show a linear relationship. approimated b real-life data points. 9. The solution to a sstem of equations is the ordered pair that 9. solves both equations. 0. The more accurate wa to solve a sstem of equations is b 0. graphing. In our own words Define each term.. vertical line test. rate of change Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

74 NAME DATE PERID Chapter Quiz (Lessons through ) SCRE. The table shows how speed affects Speed Gas Mileage. the gas mileage of one tpe of (mph) (mpg) compact car. Is the relation a 0 function? Eplain. Describe how 0 gas mileage is related to speed Find four solutions of. 70. Write the solutions as ordered pairs.. Graph the equation b plotting ordered pairs... Find the -intercept and -intercept for the graph of Graph using the - and -intercepts. NAME DATE PERID Chapter Quiz (Lessons and ) SCRE For Questions and, find the slope of the line that passes through each pair of points... A(, ) and B(, ). A(, ) and B(, 9).. Standardized Test Practice Two roller coasters are ving for the title of Steepest Drop. The first ride has a hill that drops 0 feet in a 0-foot run. The second ride s highest hill drops 0 feet in a 0-foot run. Which statement is true? A. The first ride is the Steepest Drop. B. The second ride is the Steepest Drop. C. Both rides have the same slope D. There is not enough information to tell... The table shows the results of a science eperiment.. Find the rate of change. (minutes) 0 ( F) 0 Assessment Glencoe/McGraw-Hill Glencoe Pre-Algebra

75 NAME DATE PERID Chapter Quiz (Lessons through ) SCRE For Questions and, use the equation.. State the slope and the -intercept for the graph of the equation.... Graph the equation using the slope and -intercept.. Write an equation in slope-intercept form to represent the table values. 0 The relation between the number of receivers (millions) and the time after the technolog was introduced is shown in the scatter plot.. Draw the best fit line and estimate the rate of change.. Predict the number of receivers ears after the technolog was introduced. Number of Receivers 9 Years after Introduction Number of Receivers.. 9. Years after Introduction NAME DATE PERID Chapter Quiz (Lessons 9 and 0) SCRE For Questions and, solve each sstem of equations b substitution Use the graphs of and to eplain wh the related sstem of equations has no solution.. Graph... Terika is buing drinks for a summer camp and she has $7 to spend. range juice costs $.0 per gallon and milk costs $.00 per gallon. Write an inequalit to represent this situation. Identif the variables and describe what the represent. Glencoe/McGraw-Hill Glencoe Pre-Algebra.

76 NAME DATE PERID Chapter Mid-Chapter Test (Lessons through ) SCRE Part I Write the letter for the correct answer in the blank at the right of each question.. The relation {(, 7), ( 7, ), (, ), (0, )} is not a function when which ordered pair is added to the set? A. (, 0) B. (0, ) C. (, ) D. (9, ).. Use the table shown to complete the sentence in the best wa. Generall, as increases,? A. increases B. decreases C. remains constant D. increases, decreases, then decreases.. Find the slope of the line that passes through the points A(, ) and B(, 0). A. B. C. D... The sun rises at 7: A.M. on December, 00 in Dallas and at 7: A.M. on December 7. What is the rate of change? A. minutes later each da C. minutes later per da B. minutes D. das.. Which of the following is a solution of? A. (0, ) B. (, ) C. (, 0) D. (0, ). Part II. Graph b plotting ordered pairs.. 7. Graph using the - and -intercepts. 7. Use the graph shown at the right.. What is the slope of the line?. 9. Find the - and -intercepts of the line Write a direct variation equation relating and. 0. Assessment Glencoe/McGraw-Hill Glencoe Pre-Algebra

77 NAME DATE PERID Chapter Cumulative Review (Chapters ). Simplif 7( ) ( 7). (Lesson ).. What is divided b? (Lesson ).. Find the LCM of and z. (Lesson ).. Epress miles in hours as a unit rate. (Lesson ).. If Marta bought ounces of perfume for $, how much. would ounces cost? (Lesson ). In a scale model of a boat, the tallest mast has a height of. 7 inches. If the actual height of the mast is feet, what is the scale of the model? (Lesson ) Solve each equation. (Lessons 7 and 7 ) 7. ( 9). n 7(n ) n Solve each inequalit. (Lessons 7 and 7 ) t Find two solutions to the equation 0. Write the solutions as ordered pairs. (Lesson ).. Graph b plotting ordered pairs. (Lesson ).. Find the slope of the line that passes through the points. A(, ) and B(, ). (Lesson ). State the slope and the -intercept for the graph of. 9. (Lesson ). Find the rate of change for the linear function.. (Lesson ). Solve the sstem of linear equations 7. and b substitution. (Lesson 9) Glencoe/McGraw-Hill Glencoe Pre-Algebra

78 NAME DATE PERID Standardized Test Practice (Chapters ) Part : Multiple Choice Instructions: Fill in the appropriate oval for the best answer.. Solve z for. (Lesson ) A. B. z C. z D. z. z A B C D. Ron put all his math test scores in numerical order from least to greatest and found the middle number. Which measure of central tendenc does this number represent? (Lesson ) E. mean F. median G. mode H. outlier. E F G H. Find the fifth term in the sequence,,,.... (Lesson 0) A. B. C. D.. A B C D. What value of makes 7. a proportion? (Lesson ). 9 E. F.. G. 0. H. 0.. E F G H. In December, Morristown received. inches of rain. In Januar, Morristown received.9 inches of rain. What was the percent of change from December to Januar? (Lesson ) A. % B. % C..% D..%. A B C D. Three times a number is 0 less than seven times the number. What is the number? (Lesson 7 ) E. 0 F. 0 G. H.. E F G H 7. Solve a (a 7) a. (Lesson 7 ) A. 0 B. C. all numbers D. 7. A B C D. Which inequalit represents a number increased b 7 is at most 9? (Lesson 7 ) E. n 7 F. n 7 9 G. n 7 9 H. n 7 9. E F G H 9. Solve 0. (Lesson 7 ) A. B. C. D. 9. A B C D 0. Solve. (Lesson 7 ) E. F. G. H. 0.. Find the rate of change for the linear function. (Lesson ) A. 7 B. C. D.. A B C D 7 Glencoe/McGraw-Hill Glencoe Pre-Algebra E F G H Assessment

79 NAME DATE PERID Standardized Test Practice (continued). Suppose varies directl with. If when is, what is the direct variation equation? (Lesson ) E. F. G. H.. E F G H. A linear function has slope and goes through the point (, ). What is the -coordinate of the point on the line whose -coordinate is? (Lesson 7) A. B. C. D.. A B C D. Choose the inequalit that describes the graph shown. (Lesson 0) E. F. G. H.. E F G H. Determine which ordered pair is a solution of 0. (Lesson 7) A. (, ) B. (, ) C. (, ) D. (, 9). A B C D Part : Grid In Instructions: Enter our answer b writing each digit of the answer in a column bo and then shading in the appropriate oval that corresponds to that entr.. Evaluate a b c if a, b, and c. (Lesson ) 7. Find the -intercept for the graph of. (Lesson ). 7. / / / / Part : Short Response Instructions: Write our answer in the blank at the right of each question.. Jan uses gallon of paint to cover 00 square feet of ceiling. Write a proportion that could be used to find how man gallons. she will need to cover 700 square feet. Then solve. (Lesson ) 9. Solve the sstem of linear equations and 9. b substitution. (Lesson 9) Glencoe/McGraw-Hill Glencoe Pre-Algebra

80 NAME DATE PERID Unit Test (Chapters 7 ) SCRE. Solve... Solve (a ) (a )... The perimeter of a rectangle is inches. The length is. inches less than twice the width. Find the dimensions of the rectangle.. Write an inequalit that represents the quotient when. dividing a number b 9 is less than 9.. Write an inequalit for the graph... An F- tornado has winds that are at least 9 miles per. hour. Suppose a tornado has winds that are 7 miles per hour. Write and solve an inequalit to find out how much the winds must increase before the tornado becomes an F- tornado. 7. Solve q b. Solve Three more than the quotient of a number and 7 is at most Find the number. 0. Four times the sum of a number and is at least si times 0. the same number less. For what numbers is this true?. Solve ( ). Graph our solution on a number line... The table represents the temperature at kilometers. above sea level for a certain location. Describe the relationship between the temperature and the altitude. Is this relation a function? Altitude (km) 0 Temperature ( C) Find two solutions of 0. Write the solutions as. ordered pairs. 0. Find the -intercept and -intercept of. Then. graph the equation. Assessment Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra

81 NAME DATE PERID Unit Test (continued) (Chapters 7 ). Find the slope of the line that passes through A( 7, ) and. B(, ).. The table shows the Wind (mph) Temperature ( F). wind chill temperature for different wind 0 speeds when the actual temperature is F. State the rate of change Write an equation in slope-intercept 7. form for the line graphed.. If (, b) is on the graph of the line. with slope and -intercept, find the value of b. 9. The scatter plot at the right 9. shows a correlation between and. Draw a best-fit line for the data. Use the best-fit line to predict the value of when is. 0. Solve the sstem of equations b graphing Solve the sstem of equations b substitution Graph.. Glencoe/McGraw-Hill Glencoe Pre-Algebra

82 NAME DATE PERID Standardized Test Practice Student Record Sheet (Use with pages 0 of the Student Edition.) Part Multiple Choice Select the best answer from the choices given and fill in the corresponding oval. A B C D A B C D 7 A B C D 9 A B C D Answers A B C D A B C D A B C D 0 A B C D A B C D A B C D Part Short Response/Grid In Solve the problem and write our answer in the blank. For Questions,, and 9, also enter our answer b writing each number or smbol in a bo. Then fill in the corresponding oval for that number or smbol. 9 (grid in) / /.... / /.... / / (grid in) (grid in) 0 Part pen Ended Record our answers for Question on the back of this paper. Glencoe/McGraw-Hill A Glencoe Pre-Algebra