Chapter 8 Resource Masters

Transcription

1 Chapter Resource Masters

2 Consumable Workbooks Man of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. ISBN ISBN Stud Guide and Intervention Workbook X Homework Practice Workbook Spanish Version Homework Practice Workbook Answers for Workbooks The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorks Plus This CD-RM includes the entire Student Edition test along with the English workbooks listed above. TeacherWorks Plus All of the materials found in this booklet are included for viewing, printing, and editing in this CD-RM. Spanish Assessment Masters (ISBN: , ISBN: ) These masters contain a Spanish version of Chapter Test Form A and Form C. Copright b The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such materials be reproduced onl for classroom use; be provided to students, teachers, and families without charge; and be used solel in conjunction with the Glencoe Pre-Algebra program. An other reproduction, for sale or other use, is epressl prohibited. Send all inquiries to: Glencoe/McGraw-Hill 77 rion Place Columbus, H - 7 ISBN: MHID: Printed in the United States of America

3 Contents Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Teacher s Guide to Using the Chapter Resource Masters... iv Chapter Resources Chapter Student-Built Glossar... Chapter Anticipation Guide (English)... Chapter Anticipation Guide (Spanish)... Lesson - Functions Stud Guide and Intervention... Skills Practice... 7 Practice... Word Problem Practice... 9 Enrichment... Lesson - Sequences and Equations Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... Enrichment... Lesson - Representing Linear Functions Stud Guide and Intervention... 7 Skills Practice... 9 Practice... Word Problem Practice... Enrichment... Lesson - Rate of Change Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... 7 Enrichment... Spreadsheet Activit... 9 Lesson - Constant Rate of Change and Direct Variation Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... Enrichment... Lesson - Slope Stud Guide and Intervention... Skills Practice... Practice... 9 Word Problem Practice... Enrichment... Lesson -7 Slope-Intercept Form Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... Enrichment... 7 Lesson - Writing Linear Equations Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... Enrichment... Lesson -9 Prediction Equations Stud Guide and Intervention... Skills Practice... Practice... 7 Word Problem Practice... Enrichment... 9 Lesson - Sstems of Equations Stud Guide and Intervention... Skills Practice... Practice... Word Problem Practice... Enrichment... Assessment Student Recording Sheet... Rubric for Scoring Etended Response... 7 Chapter Quizzes and... Chapter Quizzes and... 9 Chapter Mid-Chapter Test... 7 Chapter Vocabular Test... 7 Chapter Test, Form... 7 Chapter Test, Form A... 7 Chapter Test, Form B... 7 Chapter Test, Form C... 7 Chapter Test, Form D... Chapter Test, Form... Chapter Etended-Response Test... Standardized Test Practice... Answers... A A Chapter iii Glencoe Pre-Algebra

4 Teacher s Guide to Using the Chapter Resource Masters 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 TeacherWorks Plus TM CD-RM. Chapter Resources Student-Built Glossar (pages ) These masters are 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. Give this to students before beginning Lesson -. Encourage them to add these pages to their mathematics stud notebooks. Remind them to complete the appropriate words as the stud each lesson. Anticipation Guide (pages ) This master, presented in both English and Spanish, is a surve used before beginning the chapter to pinpoint what students ma or ma not know about the concepts in the chapter. Students will revisit this surve after the complete the chapter to see if their perceptions have changed. Lesson Resources Stud Guide and Intervention This master provides vocabular, ke concepts, additional worked-out eamples and Check Your Progress eercises to use as a reteaching activit. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-da teaching of the lesson. Practice This master closel follows the tpes of problems found in the Eercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for secondda teaching of the lesson. Word Problem Practice This master includes additional practice in solving word problems that appl the concepts of the lesson. Use as an additional practice or as homework for second-da teaching of the lesson. Enrichment These activities ma etend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics the are learning. The are written for use with all levels of students. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter iv Glencoe Pre-Algebra

5 Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Graphing Calculator, Scientific Calculator, or Spreadsheet Activities These activities present was in which technolog can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of our lesson presentation. Assessment ptions The assessment masters in the Chapter Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment. Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter. Etended Response Rubric This master provides information for teachers and students on how to assess performance on open-ended questions. Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter. Mid-Chapter Test This -page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and freeresponse questions. Vocabular Test This test is suitable for all students. It includes a list of vocabular words and questions to assess students knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests. Leveled Chapter Tests Form contains multiple-choice questions and is intended for use with below grade level students. Forms A and B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations. Forms C and D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations. Form is a free-response test for use with above grade level students. All of the above tests include a free-response Bonus question. Etended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation. Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and shortanswer free-response questions. Answers The answers for the Anticipation Guide and Lesson Resources are provided as reduced pages with answers appearing in red. Full-size answer kes are provided for the assessment masters. Chapter v Glencoe Pre-Algebra

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7 NAME DATE PERID Student-Built Glossar 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 Chapter Resources arithmetic (air-uth-met-ik) sequence common difference constant of variation (VEHR-ee-AY-shuhn) constant rate of change dependent variable Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. direct variation famil of functions function notation independent variable line of fit linear (LIHN-ee-uhr) equation Chapter Glencoe Pre-Algebra

8 NAME DATE PERID Student-Built Glossar (continued) Vocabular Term linear relationship Found on Page Definition/Description/Eample point-slope form rate of change sequence slope slope-intercept (IHNT-uhr-SEHPT) form substitution sstem of equations term vertical line test -intercept Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. -intercept Chapter Glencoe Pre-Algebra

9 NAME DATE PERID Anticipation Guide Linear Functions and Graphing Step Before ou begin Chapter Read each statement. Decide whether ou Agree (A) or Disagree (D) with the statement. Write A or D in the first column R if ou are not sure whether ou agree or disagree, write NS (Not Sure). Chapter Resources STEP A, D, or NS Statement. A relation is a set of ordered pairs. Step A or D. All functions are relations.. The equation - = cannot be solved because it contains two variables.. The graph of an linear equation is a straight line.. The -intercept is the point where a graph crosses the -ais. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. The slope of a line refers to the steepness of that line. 7. A vertical line has a slope of.. In the line = +, is the slope. 9. When the graphs of a sstem of equations have different slopes, then there is eactl solution to the sstem. Step After ou complete Chapter Reread each statement and complete the last column b entering an A (Agree) or a D (Disagree). Did an of our opinions about the statements change from the first column? For those statements that ou mark with a D, use a separate sheet of paper to eplain wh ou disagree. Use eamples, if possible. Chapter Glencoe Pre-Algebra

10 NMBRE FECHA PERÍD Ejercicios preparatorios Lineal Funciones graficas Paso Antes de comenzar el Capítulo Lee cada enunciado. Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado. Escribe A o D en la primera columna si no estás seguro(a) de la respuesta, escribe NS (No esto seguro(a)). PAS A, D o NS Enunciado. Una relación es un conjunto de pares ordenados.. Todas las funciones son relaciones. La ecuación - = no se puede resolver porque contiene dos variables.. La gráfica de cualquier ecuación lineal es una recta.. La intersección es el punto donde una gráfica cruza el eje. PAS A o D Paso. La pendiente de una recta se refiere a la inclinación de la misma. 7. Una recta vertical tiene una pendiente de.. En la recta = +, es la pendiente. 9. Cuando las gráficas de un sistema de ecuaciones tienen diferentes pendientes, entonces eiste eactamente solución para el sistema. Después de completar el Capítulo Vuelve a leer cada enunciado completa la última columna con una A o una D. Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna? En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Capítulo Pre-Álgebra de Glencoe

11 NAME DATE PERID - Stud Guide and Intervention Functions Relations and Functions A function is a special relation in which each element of the domain is paired with eactl one element of the range. To determine whether a relation is a function, list the domain and range of the relation and make sure that each member of the domain pairs up with onl one value in the range. Another method is to appl the vertical line test to the graph of the relation. Vertical Line Test Since functions are relations, the can be represented using ordered pairs, tables, or graphs. Eample 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. Lesson - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. a. {(-, -), (, -), (, -9), (, )} Domain () - Range () Because each element in the domain is paired with onl one value in the range, this is a function. Eercises b. Use a pencil or straightedge and move from left to right across the graph. It passes through more than one point of the graphed relation at =. Therefore, this is not a function. Determine whether each relation is a function. Eplain.. {(-, ), (, -), (, 7), (, )}. {(, 7), (-, ), (-, ), (-, ), (, )} Chapter Glencoe Pre-Algebra

12 NAME DATE PERID - Stud Guide and Intervention Functions (continued) Function Notation Functions that can be written as equations can be written in function notation, where the variable and the term f() represent the dependent variable. The term f() is read f at. equation = function notation f() = Eample f() = + f(-) = (-) + or - So, f(-) = -. If f() = +, find the function value for f(-). Write the function. Substitute for into the function rule. Eample DRIVING Janie drove miles at miles per hour. Use function notation to write an equation that gives the total mileage as a function of the number of hours driven. Then use the equation to determine the number of hours Janie drove. First write the equation. Words: miles driven = miles per hour times the number of hours Variables: Let m(h) = miles driven and h = number of hours. Function: m(h) = h The function is m(h) = h. Net, use the equation to find how man hours Janie drove. m(h) = h Write the function. = h Substitute for m(h). = h Divide each side b. So, Janie drove for hours. Eercises If f() = - +, find each function value.. f(9). f(). f(-). f(-). f(). f(-) 7. f(). f(-) If f () = -, find each function value. 9. f(). f(-). f(). f(-). f(). f(-). f(-9). f(7) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 7. PHNES Charlene s phone service costs $ a month plus $. per minute. Last month, her phone bill was $. Use function notation to write an equation that gives the total cost as a function of the number of minutes used. Then use the equation to find how man minutes Charlene used. Chapter Glencoe Pre-Algebra

13 NAME DATE PERID - Skills Practice Functions Determine whether each relation is a function. Eplain.. {(,-), (, ), (, -), (, )}. {(, ), (-, -), (-, ), (, )}. {(-, ), (, -), (, ), (, )}. {(, ), (-, ), (-, ), (-, ), (, )} Lesson Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. If f() = -, find each function value. 9. f(). f(9). f(). f(). f(-). f(-). f(). f(-) If g() = +, find each function value. 7. g(). g(7) 9. g(-). g(). g(-). g(-). g(9). g() Chapter 7 Glencoe Pre-Algebra

14 NAME DATE PERID - Practice Functions Determine whether each relation is a function. Eplain.. {(, -), (, -9), (, ), (7, )}. {(, ), (-, ), (-7, ), (, ), (, ), (-7, )} If f() = +, find each function value. 7. f(). f(-) 9. f(). f(-) EMPLYMENT For Eercises, use the table, which shows the percent of emploed men and women in the U.S. labor force ever five ears from 9 to.. Is the relation (ear, percent of men) a function? Eplain.. Describe how the percent of emploed men is related to the ear. Year. Is the relation (ear, percent of women) a function? Eplain. Emploed Members of Labor Force Men (% of male population) Women (% of female population) Source: U.S. Census Bureau Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Describe how the percent of emploed women is related to the ear. Chapter Glencoe Pre-Algebra

15 NAME DATE PERID - Word Problem Practice Functions. BEACNS Below are shirt sizes found in a department store, listed as (neck circumference, arm length). {(, ), (, ), (, ), (, ), (, ), (, ), (7, ), (7, )} Does the relation (neck size, arm length) represent a function? Eplain.. GASLINE The table below lists the average price of gasoline per gallon in the United States at the end of each month in a recent ear.. BKS The table below shows the price of a book and its page content. Price ($) Pages Does the relation (price, pages) represent a function? Eplain. Lesson - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Month Price Month Price Januar $. Jul $. Februar $. August $.7 March $. September $. April $.9 ctober $. Ma $.9 November $.7 June $.9 December $. Does the relation (month, price) represent a function? Eplain.. TAXI FARE The information listed shows the cost of a cab ride across town: Distance (miles) Price ($) Does the relationship between the distance traveled and the cost represent a function? Eplain.. EARTH S ATMSPHERE The table below shows the tpical air temperature at various altitudes. Altitude (ft) Air Temperature ( F) 9.,., -., -., -9.7, -9.7, , -9.7, , -., -. a. Eplain whether or not this relationship represents a function. b. Describe the relationship between altitude and air temperature. Chapter 9 Glencoe Pre-Algebra

16 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 () = +. f() f f() = +. g(). 7. Eplain whether the diagram below shows a transformation. 7 g 9 h h() Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

17 NAME DATE PERID - Stud Guide and Intervention Sequences and Equations Describe Sequences A sequence is an ordered list of numbers. Each number is a term of the sequence. An arithmetic sequence is a sequence in which the difference between an two consecutive terms, called the common difference, is the same. In the sequence below, the common difference is 7., 9,,,,..., Eample Describe the sequence using words and smbols.,, 9,, Term Number (n) Term (t) 9 The difference of the term numbers is. The common difference of the terms is The terms have a common difference of. A term is times the term number. So, the equation that describes the sequence is t = n. Eercises Describe each sequence using words and smbols. Lesson - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc..,,, 7,., 7,, 9,.,,,,.,,,,.,,,,. 9,, 7,, 7.,,,,., 7,,, 9.,,,, Chapter Glencoe Pre-Algebra

18 NAME DATE PERID - Stud Guide and Intervention Sequences and Equations (continued) Finding Terms The rule or equation that describes a sequence can be used to either etend the pattern or to find other terms. Eample Write an equation that describes the sequence, 7, 9,,. Then find the th term of the sequence Term Number (n) Term (t) 7 9 The difference of the term numbers is. The common difference of the terms is The terms have a common difference of. This is times the difference of the term numbers. This suggests that t = n. However, ou need to add to get the value of t. So, a term is more than times the term number. The equation that describes the sequence is t = n +. Use the equation to find the th term. Let n =. t = n + Write the equation. t = () + or Replace n with. So, the th term is. Eample Dais made the figures shown at the right with tiles. Each tile has an area of square foot. If she continues the pattern, which figure would have an area of square feet? Make a table to organize our sequence and find a rule. Term Number (t) Term (a) 7 9 The pattern in the table shows the equation a = t +. a = t + Write the equation. = t + Replace a with. Solve for t. So, figure would be a design with an area of square feet. Eercises Write an equation that describes each sequence. Then find the indicated term..,,, 9, ; th term.,,,, ; th term The difference of the term numbers is. The common difference of the terms is. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. GEMETRY Rhonda made the figures shown at the right using toothpicks. Each toothpick has a length of inch. If she continues the pattern, which figure will have a perimeter of inches? Chapter Glencoe Pre-Algebra

19 NAME DATE PERID - Skills Practice Sequences and Equations Describe each sequence using words and smbols.. 7,, 9,,.,, 7,,. 7,,,,.,,,,.,, 7, 9,.,,, 9, 7.,, 9, 7,.,, 9, 7, Lesson - Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Write an equation that describes each sequence. Then find the indicated term. 9.,,,, ; 9th term. 7,,,, ; th term. 7, 9,,, ; th term.,,,, ; th term., 7,, 9, ; th term.,,,, ; th term., 9,,, ; th term.,,, 7, ; th term Chapter Glencoe Pre-Algebra

20 NAME DATE PERID - Practice Sequences and Equations Describe each sequence using words and smbols..,,,,.,,, 9,. 9,, 9,,.,, 7,,.,, 7, 9,.,, 7, 9, Write an equation that describes each sequence. Then find the indicated term. 7.,,, 9, ; 7th term. 9,, 7,, ; st term 9.,,, 7, ; th term., 7, 7, 7, ; th term., 9,,, ; 7th term.,,, 9, ; 7th term. RUNNING Luisa ran miles on the rd da of a month, and she repeated her run ever das for the rest of the month. What equation describes the sequence of das of that month that Luisa ran? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. DEPRECIATIN A new hbrid car costs $,. If it depreciates at $ of its value each ear, find the value of the car over the net ears. Chapter Glencoe Pre-Algebra

21 NAME DATE PERID - Word Problem Practice Sequences and Equations. GAS CNSUMPTIN Mr. Haskell kept track of how much gasoline his car was using. He displaed the data collected in a table. Gallons Used Miles Driven n 9? Write an equation that Mr. Haskell can use to find how man miles he can drive with gallons of gas in his car.. TRIANGULAR NUMBERS B arranging bowling pins in their proper order, a triangle is created. The table below shows the number of rows of bowling pins and the total number of pins in the triangle. The formula t = n (n + ) can be used to find t, the total number of items in n rows. How man bowling pins would there be if rows of pins were set up? Rows Pins Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. HBBIES Shannon collects charms for her charm bracelet. Her charm bracelet had charms on it when she bought it. Each ear on her vacation she bus more charms to add to her bracelet. Assume that Shannon continues to bu the same number of charms each ear. Write an equation that can be used to find how man charms Shannon will have on her bracelet after ears?. PYRAMIDS When climbing an ancient Maan pramid, the Johnson famil noticed that the bottom of each side of the pramid started with large stones. The net level up had large stones, the net level up had stones, and so on. Write an equation to represent the number of stones on each level. How man levels can the pramid have? Level Stones?. PASCAL S TRIANGLE Blaise Pascal is known for a special triangular arrangement of numbers, called Pascal s Triangle. Each number in successive rows of the triangle is created b adding the two numbers in the row above the number. a. Starting with the second row from the top, what is the sequence of the diagonal ( 7)? b. The sum of each row represents n-, which means is multiplied b itself n - times, where n represents the row number. Write an epression for the sum of the values in the sith row. Simplif the epression. Lesson - Chapter Glencoe Pre-Algebra

22 NAME DATE PERID - Enrichment Applications of Geometric Sequences Populations often grow according to a geometric sequence, which is the sequence in which the quotient of an two consecutive terms is the same. If the population of a cit grows at the rate of % per ear, then the common ratio, r, is.. To find the population of a cit of, after ears of % growth, use the formula ar n-, where r is the common ratio and n is the number of ears. ar n- =, (.) - =, (.), So, the cit has a population of, people. After a few ears, a small change in the annual growth rate can cause enormous differences in the population. Assume that the nation of Grogro had a population of one million in. Using a calculator, find the population of the countr in the ears, 7, and at growth rates of %, %, and % per ear. Record our results in the table below. Growth Rate. %. %. % Suppose we want to find the total upward distance a bouncing ball has moved. It bounces up inches on the first bounce and times its height on each of five more consecutive bounces. st bounce nd bounce rd bounce in. 7 in. in. The distances form the terms of a geometric sequence. We want to find the sum of the distances, or the sum of the si terms in the sequence. The sum of the terms of a geometric sequence is called a geometric series. The formula for the sum S n of the first n terms of a geometric series is S n = a - a r n where a = the first term - r and r = the common ratio (r ). S n = a - a r n - r = - ( ) -. Write the formula. a =,, r =., n = a =, r =, n = Population of Grogro Year 7 So, the ball bounces upward approimatel. inches. Use the formula above to find each sum. Then check our answer b adding. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Chapter Glencoe Pre-Algebra

23 NAME DATE PERID - Stud Guide and Intervention Representing Linear Functions Solve Linear Equations An equation whose graph is a line is called a linear equation. Eamples of linear equations are given below. = = + 7 = = - A linear equation is also a function because each member of the domain (-value) is paired with eactl one member of the range (-value). Solutions to a linear equation are ordered pairs that make the equation true. ne wa to find solutions to an equation is to make a table. Eample Find four solutions of = -. Write the solutions as ordered pairs. Step Choose four values for and substitute each value into the equation. We choose -,,, and. Step Evaluate the epression to find the value of. Step Write the solutions as ordered pairs. = - (, ) - = (-) - - (-, -) = () - - (, -) = () - - (, -) = () - - (, -) Four solutions of = - are (-, -), (, -), (, -), and (, -). Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eercises Cop and complete each table. Use the results to write four ordered pair solutions of the given equation.. = +. = - = + = Find four solutions of each equation. Write the solutions as ordered pairs.. = 9 -. = +. = - 7 Lesson -. = + 7. = = Chapter 7 Glencoe Pre-Algebra

24 NAME DATE PERID - Stud Guide and Intervention Representing Linear Functions Graph Linear Equations You can plot points on a coordinate plane to graph a linear equation. You can find ordered pairs using a table, or ou can plot the -intercept and the -intercept and connect the two points. The -intercept is the -coordinate of the point at which the graph crosses the -ais. The -intercept is the -coordinate of the point at which the graph crosses the -ais. (continued) -intercept -intercept Eample Graph + =. You can graph an equation b using a table to find ordered pairs. Step Rewrite the equation b solving for. = (, ) + = Write the equation. - = - (-) (-, ) - + = - Subtract from each side. = - () (, ) = Simplif. = - () (, ) Step Choose four values for and find the = - () (, ) corresponding values for. Four solutions (-, ) are (-, ), (, ), (, ) and (, ). Step Graph the ordered pairs on a coordinate plane and draw a line through the points. Eercises Graph each equation b plotting ordered pairs.. = -. = = = (, ) (, ) (, ) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

25 NAME DATE PERID - Skills Practice Representing Linear Functions Find four solutions of each equation. Write the solutions as ordered pairs.. = -. = =. - = -. = 7 -. = =. - = 9. - = Graph each equation b plotting ordered pairs.. = -. = - +. = - + Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. = - -. = -. = = - 7. = - +. = Lesson - Chapter 9 Glencoe Pre-Algebra

26 NAME DATE PERID - Practice Representing Linear Functions Find four solutions of each equation. Write the solutions as ordered pairs.. = -. = -7. = =. = = Graph each equation b plotting ordered pairs. 7. = -. = = = 7. = - 9. = 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 =. describes the approimate number of ounces in grams.. Find three ordered pairs of values that satisf this equation.. Draw the graph that contains these points.. Do negative values of make sense in this case? Eplain unces 7 Grams Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

27 NAME DATE PERID - Word Problem Practice Representing Linear Functions. CURRENCY n Januar,, the equation.99 = d represented the relationship between the U. S. dollar d and the British pound sterling p. Complete the following table. UK Pounds US Dollars. CAR RENTAL The cost of renting a car from the Frugal Car Rental Compan includes a $ non-refundable deposit and a travel cost of per mile. Find an equation to represent the total cost, C, if a car is rented and driven n miles. Then, find two ordered pairs that satisf this condition.. Source: XE. MEASUREMENT The equation c =.i can be used to convert between inches i and centimeters c. Complete the three ordered pairs (i, c) below. Round our answers to the nearest hundredth. (9., ), (,.), (., ).. CARNIVAL PRIZES Melissa is buing prizes for a school carnival. At the store, she finds colorful note paper sold in packs containing sheets and stickers sold individuall. She needs prizes altogether. a. Melissa uses the equation p + s = to help plan her purchase. Find three ordered pairs (p, s) that satisf this condition, and use them to graph the relationship. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. GEMETRY Jerr bought material for a fence to put around the garden shown in the drawing. Garden House The equation + = describes the relationship between the width and the length of his garden in feet. Find one ordered pair solution that makes sense in the situation and one that does not. Eplain our choices. b. Complete the following ordered pair: (, ). Does this make sense for Melissa s purchase? Eplain. Lesson - Chapter Glencoe Pre-Algebra

28 NAME DATE PERID - Enrichment Equations with Two Variables Complete the table for each equation.. = 7 +. = +. = = -. =. = = 9 -. = + 9. = +. =. = -. = Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. - Chapter Glencoe Pre-Algebra

29 NAME DATE PERID - Stud Guide and Intervention Rate of Change Rate of Change A rate of change is a rate that describes how one quantit changes in relation to another quantit. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eample rate of change = Eercises Find the rate of change for the linear function represented in the graph. rate of change = Find the rate of change for each linear function.. Pages Read 7 (, ) Eample Time (min). Cookies Needed. Cookies = = change in pages read change in time pages - pages minutes - minutes pages minutes = page per minute So, the rate of change is page/minute, or an increase of page per minute increase in time. Find the rate of change for the linear function represented in the table. change in temperature change in time = or Number of People (, ) Time (h) Distance Flown (mi) Items Sold Time (h) Temperature ( C) Sales 9 Price ($) Lesson - Chapter Glencoe Pre-Algebra

30 NAME DATE PERID - Stud Guide and Intervention (continued) Rate of Change Interpret Rates of Change You can calculate rates of change to solve problems. Eample EXERCISE The graph shows Leila and Joseph s heart rates during the minutes after the eercised. Compare the rates of change. Leila s Heart Rate: change in rate of change = change in - = = 7 - So, the rate of change is beats per minute. Joseph s Heart Rate: change in rate of change = change in - 7 = = 9 - So, the rate of change is beats per minute. Joseph s heartbeat decreased at a greater rate than Leila s heartbeat. Heart Rate Heart Rates Joseph Leila Minutes Eercises. SCIENCE Ned boiled beakers of water. He put beaker in a pot of cold water to cool. The table shows the temperature in the two beakers. Compare the rates of change.. CARS The graph at the right shows the speed at which two cars accelerated from miles per hour. Compare the rates of change. Speed (mph) Time Temperature ( C) (m) Beaker Beaker Acceleration Car Car 7 9 Time (s) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

31 NAME DATE PERID - Skills Practice Rate of Change Find the rate of change for each linear function... Amount of Milk (L) 7 9 Week Year Salar ($),,,,.. Savings ($) Month Number of Emploees Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Year. Time (min) Temperature ( C). 9 7 Price ($) Price of Bulk Food Weight (lbs) Lesson - Chapter Glencoe Pre-Algebra

32 NAME DATE PERID - Practice Rate of Change Find the rate of change for each linear function... Air in Tires (psi) Time (h) Distance (km) Time (min) TRADE The graph shows the total U.S. eports from 97 to.. Find the approimate rate of change between 97 and 97.. Find the approimate rate of change between and.. Between which two ears was the rate of change the least? TRAFFIC MANAGEMENT For Eercises and 7, use the following information. Eports (billions of dollars) 9 7 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 increases with the number of cars on the road. The table shows a sample of possible tolls.. Find the rate of change in the toll between vehicles/h and vehicles/h. 7. Find the rate of change in the toll between vehicles/h and vehicles/h. U.S. Eports Year Toll ($) Traffi c Volume (vehicles/h).... Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

33 NAME DATE PERID - Word Problem Practice Rate of Change. AVIATIN An airplane was at an altitude of, feet minutes before landing, and at an altitude of feet minutes before landing. What was the rate of change of the plane s altitude per minute?. TICKET SALES A ticket sales representative at a local water park had $7. in his cash register at the end of his first hour at work. If each ticket to the park cost $.7, and he sold an average of one ticket per minute, how much was in his register to start?. STAMPS Kuri needs $. in postage to mail some photographs to a friend. She has and 9 stamps. The table shows some combinations of and 9 stamps that she could use to mail the letter. Find the rate of change between the numbers of stamps and 9 stamps. 9 stamps stamps 9. PPULATIN The table shows how residential patterns in the United States have changed over the past ears. Year Urban Population (per ) Rural Population (per ) 9. BASEBALL This graph shows the total number of runs that the Boston Red So scored during the 99-7 seasons. a. Find the greatest rate of change between two seasons. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Source: Census Bureau Compare the rates of change for each time interval, and describe how the population has changed since. Runs Year b. Find the average rate of change from 99 to. Lesson - Chapter 7 Glencoe Pre-Algebra

34 NAME DATE PERID - Enrichment Fibonacci Sequence The first fifteen terms of the Fibonacci sequence are shown below.,,,,,,,,,, 9,,, 77, 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.. Find the sum of the first five terms.. Find the sum of the first si terms.. What is the relationship between the sums and terms in the sequence?. Use our answer from Eercise above to predict the sum of the first terms, and of the first terms. Check our answers b finding the sums.. Divide each of the first terms b. Make a list of the remainders. What pattern do ou see in the remainder sequence? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

35 NAME DATE PERID - Spreadsheet Activit Circles and Rates of Change You can use a spreadsheet to investigate the relationship between the radius and the circumference of a circle. Step Use a tape measure to measure the radius and the circumference of several circular objects. Enter the data into a spreadsheet like the one shown at the right. Step Use the chart tool to create a graph to eamine the data. Select the data in columns A and B and select Chart from the Insert menu. Select an XY (Scatter) chart to show the data points. Circles.ls 7 A Radius B Circumference Sheet Sheet Sheet Step Add a trendline to the graph b choosing the Chart menu. Add a linear trendline.use the options menu to have the trendline forecast backward in order to show the -intercept. For eample, if our least diameter is units, forecast backward units. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eercises. Estimate the slope of the trendline.. What should the slope of the line be? Eplain.. Is this relationship a direction variation? Eplain. Lesson - Chapter 9 Glencoe Pre-Algebra

36 NAME DATE PERID - Stud Guide and Intervention Constant Rate of Change and Direct Variation Constant Rates of Change Relationships that have a straight-line graph are called linear relationships. A linear relationship has a constant rate of change, which means that the rates of change between an two data points is the same. In a given linear relationship, if the ratio of each non-zero -value to the corresponding -value is the same, the linear relationship is also proportional. Eample GARDENS Gina recorded the height of a tomato plant in her garden. Find the constant rate of change for the plant s growth in the graph shown. Describe what the rate means. Then determine whether there is a proportional linear relationship between the plant height and the time. Step Choose an two points on the line, such as (, ) and (7, ). (, ) weeks, height in. (7, ) 7 weeks, height in. Step Find the rate of change between the points. Height (in.) Height of Tomato Plant 7 9 Weeks rate of change = = change in height change in time. in. - in. 7 wk - wk =. in./wk = in. wk The rate of change. in./wk means the plant is growing at a rate of. inches per week. To determine if the quantities are proportional, find the height for points on the graph. time in. wk.7 in./wk in. wk = in./wk in.. in./wk 7 wk The ratios are not equal, so the linear relationship is not proportional. Eercise. Find the constant rate of change for the linear function at the right and interpret its meaning. Then determine whether a proportional linear relationship eists between the two quantities. Eplain our reasoning. The height goes from in. to in. The time goes from weeks to 7 weeks. Epress this as a unit rate. Price Rice Prices Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Pounds Chapter Glencoe Pre-Algebra

37 NAME DATE PERID - Stud Guide and Intervention (continued) Constant Rate of Change and Direct Variation Direct Variation When the ratio of two variable quantities is constant, their relationship change is called a direct variation. The graph of a direct variation alwas passes through the origin and can be epressed as = k, where k is called the constant of variation, or constant of proportionalit. Eample SCUBA DIVING As scuba divers descend below the surface of the ocean, the pressure that the feel from the water varies directl with the depth. a. Write an equation that relates the depth and the amount of water pressure. Step Find the value of k using the equation = k. Choose an point in the table. Then solve for k. = k Direct variation equation 7. = k() Replace with 7. and with.. = k Simplif. Step Use k to write an equation. = k =. Replace k with.. Direct variation equation Depth (ft) Water Pressure (lb/ in ) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. b. Predict what the pressure will be at feet. =. =.() Replace with. =. Simplif. The depth at feet will be. lb/i n. Eercises Write the direct variation equation.. MNEY The amount that Jared earns ever week varies directl with the number of hours that he works. Suppose that last week he earned $7 for hours of work. Write an equation that could be used to find how much Jared earns per hour. Then find out how much Jared would earn if he worked hours.. GASLINE The cost of buing gas varies directl with the number of gallons purchased. Suppose that Lena bought. gallons of gas for $.99. Write an equation that could be used to find the unit cost per gallon of gas. Then find out how much 9. gallons of gas would cost. Round to the nearest cent.. GEMETRY The circumference of a circle is in direct variation with the diameter of the circle. Kwan drew a circle with a circumference of 7. inches and a diameter of inches. Write an equation that relates the circumference to the diameter. Use the equation to find the circumference of a circle with a -inch diameter. Lesson - Chapter Glencoe Pre-Algebra

38 NAME DATE PERID - Skills Practice Constant Rate of Change and Direct Variation Find the constant rate of change for each linear function and interpret its meaning.. Gallons Quarts. Allowance Allowance ($) 9 Age (ears). Teachers Number of Teachers Determine whether a proportional linear relationship eists between the two quantities shown in each of the functions indicated. Eplain our reasoning.. Eercise. Eercise 7. Eercise. Eercise Students. Width (ft) Height (in.) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

39 NAME DATE PERID - Practice Constant Rate of Change and Direct Variation Find the constant rate of change for each linear function and interpret its meaning.. Fundraiser Profits. Profit ($) 9 7 Cars Washed Time (seconds) Distance (ards).... Determine whether a proportional linear relationship eists between the two quantities shown in each of the functions indicated. Eplain our reasoning.. Eercise Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Eercise PAPER CSTS The cost of paper varies directl with the number of reams bought. Suppose reams cost $... Write an equation that could be used to find the cost of reams of paper.. Find the cost of reams of paper. PHYSICAL SCIENCE Recall that the length a spring stretches varies directl with the amount of weight attached to it. A certain spring stretches cm when a -gram weight is attached. 7. Write a direct variation equation relating the weight and the amount of stretch.. Estimate the stretch of the spring when it has a -gram weight attached. Lesson - Chapter Glencoe Pre-Algebra

40 NAME DATE PERID - Word Problem Practice Constant Rate of Change and Direct Variation. WATER USE The graph shows the number of quarts of water the tpical person needs in a certain number of das. Find the constant rate of change for the relationship and interpret its meaning.. TRANSPRTATIN The distance a bus travels varies directl with time. A Red Lines bus has been traveling for. hours and has traveled a distance of. miles. The total distance it must cover on a particular route is miles. How long will the bus take to cover this distance? Water needed (qt) Das. HIKING Jennifer and a group of her friends are planning a hiking trip. Jennifer is in charge of making trail mi that will provide the group a total of Calories. The graph shows the amount of peanuts and raisins she would have to bu in order to make the trail mi as planned. Source: National Park Service. BAKING The amount of flour needed for a recipe varies directl with the number of servings planned. Three servings require cups of flour. Write a direct variation equation relating the number of servings s and the required number of cups of flour f.. SCUBA DIVING Fresh Air Scuba Compan leases scuba diving equipment. The following table shows the cost of renting equipment for different lengths of time. Determine if there is a Das 9 Cost ($) 7 9 proportional relationship between the cost of the rental and the number of das the equipment is rented. Eplain. Raisins (oz) Peanuts (oz) a. Find the constant rate of change for this linear function and interpret its meaning. b. Determine if a proportional relationship eists between ounces of peanuts and ounces of raisins. Eplain. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Pre-Algebra

41 NAME DATE PERID - Enrichment Curves With Varing Rates of Change 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. Step Make a table of ordered pairs that satisf the equation. Step Graph each point. Step Draw a smooth curve connecting the points. Sketch a smooth curve through the points shown. The right side of the first curve has been done for ou.... = = - = Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Graph each equation.. =. = +. = Lesson - Chapter Glencoe Pre-Algebra

42 NAME DATE PERID - Stud Guide and Intervention Slope Slope Slope describes the steepness of a line. It is the ratio of the rise, or vertical change, to the run, or horizontal change, of a line. slope = rise run vertical change horizontal change Eample MDEL CARS Find the slope of a ramp designed to race model cars that rises inches for ever horizontal change of inches. slope = rise run = in. in. = Write the formula for slope. rise = in., run = in. Simplif. The slope of the ramp is or.7. Eample Find the slope of each line. inches inches a. b. (-, ) rise: = slope = rise run = Eercises rise: =- run: = (, -) slope = rise run = - or -. What is the slope of a hill that rises feet for ever horizontal change of feet? Write as a fraction in simplest form.. Mr. Watson is building a staircase. What is the slope of the staircase if it rises inches for ever horizontal change of inches? Write as a fraction in simplest form. Find the slope of each line.... (-, ) run: = (, ) (, ) (, ) (-, -) (, ) (-, ) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. (, -) Chapter Glencoe Pre-Algebra

43 NAME DATE PERID - Stud Guide and Intervention Slope (continued) Slope and Constant Rate of Change Note that the slope is the same for an two points on a straight line. It represents a constant rate of change. Words The slope m of a line passing through points (, ) and (, ) is the ratio of the difference in the -coordinates to the corresponding difference in -coordinates. Smbols m = - -, where Model rise (, ) run (, ) Lesson - Horizontal lines have a slope of. m = - - = - - (-) = or. Vertical lines have an undefined slope. m = - - = - (-) = - Division b is undefined. (-, ) (, ) (, -) Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eample m = - - m = m = The slope is. Eercises Find the slope of the line that passes through I(9, ) and U(, ). Definition of slope (, ) = (, ), (, ) = (9, ) Simplif. I(9, ) U(, ) Find the slope of the line that passes through each pair of points.. A(, ), B(-, ). L(, ), M(, ). R(7, -), S(7, ). Q(, 9), R(-, ). C(-, ), D(, ). S(-, -), T(, ) 7. G(, 7), H(, 7). D(, ), E(-, -) 9. K(, -), L(-, ) - - Chapter 7 Glencoe Pre-Algebra

44 NAME DATE PERID - Skills Practice Slope Find the slope of each line.. (, ).. (, ) (, ) (, ) (, -) (, -).. (, ). (, ) (, ) (, ) (, -) (, -) Find the slope of the line that passes through each pair of points. 7. A(, - ), B(, - 7). C(7, - ), D(, ) 9. E(7, ), F(, ). G(, - ), H(, - ). J(, - 9), K(, - ). L(-, ), M(, ). P(, - ), Q(7, - ). R(-, - ), S(-, ). T(, - ), U(, - ). P(, - ), Q(, - ) 7. R(, - ), S(7, ). T(, ), U(7, ) 9. 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? Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 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? Chapter Glencoe Pre-Algebra