Chapter 5 Resource Masters

Transcription

1 Chapter Resource Masters

2 CNSUMABLE WRKBKS 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) 0-0--X Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Reading to Learn Mathematics Workbook ANSWERS FR WRKBKS The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorks This CD-RM includes the entire Student Edition tet along with the English workbooks listed above. TeacherWorks All of the materials found in this booklet are included for viewing and printing in the Glencoe Algebra TeacherWorks CD-RM. Glencoe/McGraw-Hill 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, teachers, and families without charge; and be used solel in conjunction with Glencoe Algebra. An other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: The McGraw-Hill Companies rion Place Columbus, H 0-0 ISBN: Glencoe Algebra Chapter Resource Masters

3 Contents Vocabular Builder vii 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 - 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 - 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 - Stud Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Chapter Assessment Chapter Test, Form Chapter Test, Form A Chapter Test, Form B Chapter Test, Form C Chapter Test, Form D Chapter Test, Form Chapter pen-ended Assessment Chapter Vocabular Test/Review Chapter Quizzes & Chapter Quizzes & Chapter Mid-Chapter Test Chapter Cumulative Review Chapter Standardized Test Practice.. Standardized Test Practice Student Recording Sheet A ANSWERS A A Glencoe/McGraw-Hill iii Glencoe Algebra

4 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 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 T USE Give these pages to students before beginning Lesson -. Encourage them to add these pages to their Algebra Stud Notebook. Remind them to add definitions and eamples as the complete each lesson. Stud Guide and Intervention Each lesson in Algebra addresses two objectives. There is one Stud Guide and Intervention master for each objective. WHEN T 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 T 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 T 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 T 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 T USE These ma be used as etra credit, short-term projects, or as activities for das when class periods are shortened. Glencoe/McGraw-Hill iv Glencoe Algebra

5 Assessment ptions The assessment masters in the Chapter Resources 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 Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of algebra concepts in various formats, which ma appear on the standardized tests that the ma encounter. This practice includes multiplechoice, grid-in, and quantitativecomparison 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. 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. Glencoe/McGraw-Hill v Glencoe Algebra

6 Reading to Learn Mathematics Vocabular Builder This is an alphabetical list of the ke vocabular terms ou will learn in Chapter. As ou stud the chapter, complete each term s definition or description. Remember to add the page number where ou found the term. Add these pages to our Algebra Stud Notebook to review vocabular at the end of the chapter. Vocabular Term constant of variation Found on Page Definition/Description/Eample Vocabular Builder direct variation famil of graphs line of fit linear etrapolation ihk STRA puh LAY shun linear interpolation ihn TUHR puh LAY shun negative correlation KAWR uh LAY shun parallel lines (continued on the net page) Glencoe/McGraw-Hill vii Glencoe Algebra

7 Reading to Learn Mathematics Vocabular Builder (continued) Vocabular Term perpendicular lines PUHR puhn DIH kuh luhr Found on Page Definition/Description/Eample point-slope form positive correlation rate of change scatter plot slope slope-intercept form IHN tuhr SEHPT Glencoe/McGraw-Hill viii Glencoe Algebra

8 - Find Slope Stud Guide and Intervention Slope Slope of a Line rise m or m, where (, ) and (, ) are the coordinates run of an two points on a nonvertical line Eample Eample Find the slope of the line that passes through (, ) and (, ). Let (, ) (, ) and (, ) (, ). m ( ) Slope formula,,, Simplif. Find the value of r so that the line through (0, r) and (, ) has a slope of. m Slope formula r 0 m,, r,, 0 r Simplif. ( ) ( r) Cross multipl. r Distributive Propert r r Divide each side b. Subtract from each side. Lesson - Eercises Find the slope of the line that passes through each pair of points.. (, 9), (, ). (, ), (, ). (, ), (, ). (, ), (, 9). (, ), (, ). (, ), (, ). (, ), (, ). (, ), (, ) 9. (,.), (,.) Determine the value of r so the line that passes through each pair of points has the given slope. 0. (, ), (r, ), m. (, ), (, r), m. (, ), (r, ) m. (, ), (, r), m 0. (r, ), (, ), m. (, ), (r, 9), m. (0, r), (, ), m. (0, ), (, r), m 0.. (r, ), (, r), m Glencoe/McGraw-Hill Glencoe Algebra

9 - Stud Guide and Intervention (continued) Slope Rate of Change The rate of change tells, on average, how a quantit is changing over time. Slope describes a rate of change. Eample PPULATIN The graph shows the population growth in China. a. Find the rates of change for 90 9 and for change in population : change in time or 0.0 change in population : change in time or 0.0 Population Growth in China People (billions) * Year *Estimated Source: United Nations Population Division b. Eplain the meaning of the slope in each case. From 90 9, the growth was 0.0 billion per ear, or. million per ear. From 9 000, the growth was 0.0 billion per ear, or. million per ear. c. How are the different rates of change shown on the graph? There is a greater vertical change for 90 9 than for Therefore, the section of the graph for 90 9 has a steeper slope. Eercises LNGEVITY The graph shows the predicted life epectanc for men and women born in a given ear.. Find the rates of change for women from and Find the rates of change for men from and Eplain the meaning of our results in Eercises and.. What pattern do ou see in the increase with each -ear period? Predicting Life Epectanc Age * 00* Year Born Women Men *Estimated Source: USA TDAY. Make a prediction for the life epectanc for Eplain how ou arrived at our prediction. Glencoe/McGraw-Hill Glencoe Algebra

10 - Skills Practice Slope Find the slope of the line that passes through each pair of points.... (, ) (0, ) (0, ) (, ) (0, 0) (, ). (, ), (, ). (, ), (, ). (, ), (, ). (, ), (, ) Lesson -. (, ), (, ) 9. (9, ), (, ) 0. (, ), (, ). (, 0), (, ). (, ), (, ). (, ), (, ). (0, 0), (, ). (, ), (, ). (, 9), (, ). (, ), (, ). (, ), (, ) 9. (, ), (, ) Find the value of r so the line that passes through each pair of points has the given slope. 0. (r, ), (, 9), m. (, 9), (r, ), m. (r, ), (, ), m. (r, ), (, ), m. (, ), (r, ), m. (, r), (, ), m 0 Glencoe/McGraw-Hill Glencoe Algebra

11 - Practice Slope Find the slope of the line that passes through each pair of points.... (, ) (, ) (, ) (, ) (, 0) (, ). (, ), (, ). ( 9, ), (, ). (, ), (, ). (, ), (, ). (, ), (, ) 9. (, 9), (, 9) 0. (, ), (, ). (, 9), (, ). (, ), (, ). (, 0), (, ). (0., 0.9), (0., 0.9).,,, Find the value of r so the line that passes through each pair of points has the given slope.. (, r), (, ), m. (, ), (r, ), m 9. (, ), (, r), m 9. (, r), (, ), m 0. (, ), (r, ), m undefined. (, ), (, r), m. (r, ), (, ), m. (r, ), (, r), m 0. RFING The pitch of a roof is the number of feet the roof rises for each feet horizontall. If a roof has a pitch of, what is its slope epressed as a positive number?. SALES A dail newspaper had, subscribers when it began publication. Five ears later it had 0,00 subscribers. What is the average earl rate of change in the number of subscribers for the five-ear period? Glencoe/McGraw-Hill Glencoe Algebra

12 - NAME Reading to Learn Mathematics Slope DATE PERID Pre-Activit Wh is slope important in architecture? Read the introduction to Lesson - at the top of page in our tetbook. Then complete the definition of slope and fill in the boes on the graph with the words rise and run. rise slope run In this graph, the rise is units, and the run is units. units Thus, the slope of this line is or. units Reading the Lesson. Describe each tpe of slope and include a sketch. Tpe of Slope Description of Graph Sketch positive The graph rises as ou go from left to right. Lesson - negative The graph falls as ou go from left to right. zero The graph is a horizontal line. undefined The graph is a vertical line.. Describe how each epression is related to slope. a. difference of -coordinates divided b difference of corresponding -coordinates rise b. how far up or down as compared to how far left or right run $,000 increase in spending months c. slope used as rate of change Helping You Remember. The word rise is usuall associated with going up. Sometimes going from one point on the graph does not involve a rise and a run but a fall and a run. Describe how ou could select points so that it is alwas a rise from the first point to the second point. Sample answer: If the slope is negative, choose the second point so that its -coordinate is less than that of the first point. Glencoe/McGraw-Hill Glencoe Algebra

13 - Enrichment Treasure Hunt with Slopes Using the definition of slope, draw lines with the slopes listed below. A correct solution will trace the route to the treasure. Treasure Start Here no slope Glencoe/McGraw-Hill Glencoe Algebra

14 - Stud Guide and Intervention Slope and Direct Variation Direct Variation A direct variation is described b an equation of the form k, where k 0. We sa that varies directl as. In the equation k, k is the constant of variation. Eample Eample Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. For, the constant of variation is. m Slope formula 0 0 (, ) (0, 0), (, ) (, ) The slope is. Simplif. (, ) (0, 0) Suppose varies directl as, and 0 when. a. Write a direct variation equation that relates and. Find the value of k. k Direct variation equation 0 k() Replace with 0 and with. k Divide each side b. Therefore, the equation is. b. Use the direct variation equation to find when. Direct variation equation Replace with. Divide each side b. Therefore, when. Lesson - Eercises Name the constant of variation for each equation. Then determine the slope of the line that passes through each pair of points.... (, ) (0, 0) (, ) (0, 0) (, ) (0, 0) Write a direct variation equation that relates to. Assume that varies directl as. Then solve.. If when, find when.. If 9 when, find when.. If. when., find when.. If when, find when. Glencoe/McGraw-Hill Glencoe Algebra

15 - Solve Problems The distance formula d rt is a direct variation equation. In the formula, distance d varies directl as time t, and the rate r is the constant of variation. Eample TRAVEL A famil drove their car miles in hours. a. Write a direct variation equation to find the distance traveled for an number of hours. Use given values for d and t to find r. d rt riginal equation r() d and t r Divide each side b. Therefore, the direct variation equation is d t. b. Graph the equation. The graph of d t passes through the origin with slope. rise m run CHECK (, ) lies on the graph. c. Estimate how man hours it would take the famil to drive 0 miles. d t riginal equation 0 t Replace d with 0. t Divide each side b. Therefore, it will take hours to drive 0 miles. Eercises Stud Guide and Intervention (continued) Slope and Direct Variation Distance (miles) d Automobile Trips d t (, ) 90 (, ) 0 t Time (hours) RETAIL The total cost C of bulk jell beans is $.9 times the number of pounds p.. Write a direct variation equation that relates the variables.. Graph the equation on the grid at the right.. Find the cost of pound of jell beans. Cost (dollars) Cost of Jell Beans C 0 w Weight (pounds) CHEMISTRY Charles s Law states that, at a constant pressure, volume of a gas V varies directl as its temperature T. A volume of cubic feet of a certain gas has a temperature of 00 (absolute temperature).. Write a direct variation equation that relates the variables.. Graph the equation on the grid at the right.. Find the volume of the same gas at 0 (absolute temperature). Volume (cubic feet) V Charles s Law T Temperature ( K) Glencoe/McGraw-Hill Glencoe Algebra

16 - Skills Practice Slope and Direct Variation Name the constant of variation for each equation. Then determine the slope of the line that passes through each pair of points.... (, ) (, ) (0, 0) (0, 0) (, ) (0, 0) Graph each equation.... Write a direct variation equation that relates and. Assume that varies directl as. Then solve.. If when, find. If when, find when. when. Lesson - 9. If when, find 0. If 9 when, find when. when.. If when, find. If when, find when. when. Write a direct variation equation that relates the variables. Then graph the equation.. TRAVEL The total cost C of gasoline. SHIPPING The number of delivered tos T is $.0 times the number of gallons g. is times the total number of crates c. Cost ($) C 0 Gasoline Cost Tos T 9 Tos Shipped 0 0 g Gallons 0 c Crates Glencoe/McGraw-Hill 9 Glencoe Algebra

17 - NAME Name the constant of variation for each equation. Then determine the slope of the line that passes through each pair of points.. ;. ;. ; DATE PERID Practice (Average) Slope and Direct Variation (, ) (, ) (, ) (0, 0) (0, 0) (0, 0) Graph each equation.... Write a direct variation equation that relates and. Assume that varies directl as. Then solve.. If. when 0., find when 0.. ;.. If 0 when, find when 00..; 0 9. If when, find when. ; Write a direct variation equation that relates the variables. Then graph the equation. 0. MEASURE The width W of a. TICKETS The total cost C of tickets is rectangle is two thirds of the length. $.0 times the number of tickets t. W Rectangle Dimensions C.0t Width W Length. PRDUCE The cost of bananas varies directl with their weight. Miguel bought pounds of bananas for $.. Write an equation that relates the cost of the bananas to their weight. Then find the cost of pounds of bananas. C 0.p; $. Glencoe/McGraw-Hill 90 Glencoe Algebra

18 - NAME DATE PERID Reading to Learn Mathematics Slope and Direct Variation Pre-Activit How is slope related to our shower? Read the introduction to Lesson - at the top of page in our tetbook. How do the numbers in the table relate to the graph shown? The are the coordinates of the points on the graph. Think about the first sentence. What does it mean to sa that a standard showerhead uses about gallons of water per minute? Sample answer: For each minute the shower runs, gallons of water come out. So, if the shower ran 0 minutes, that would be 0 gallons. Reading the Lesson. What is the form of a direct variation equation? k. How is the constant of variation related to slope? The constant of variation has the same value as the slope of the graph of the equation. Lesson -. The epression varies directl as can be written as the equation k. How would ou write an equation for w varies directl as the square of t? w kt. For each situation, write an equation with the proper constant of variation. a. The distance d varies directl as time t, and a cheetah can travel feet in second. d t b. The perimeter p of a pentagon with all sides of equal length varies directl as the length s of a side of the pentagon. A pentagon has sides. p s c. The wages W earned b an emploee var directl with the number of hours h that are worked. Enrique earned $.0 for hours of work. W $.0h Helping You Remember. Look up the word constant in a dictionar. How does this definition relate to the term constant of variation? Sample answer: Something unchanging; the constant of variation relates and in the same value ever time, and that relationship never changes. Glencoe/McGraw-Hill 9 Glencoe Algebra

19 - Enrichment nth Power Variation An equation of the form k n, where k 0, describes an nth power variation. The variable n can be replaced b to indicate the second power of (the square of ) or b to indicate the third power of (the cube of ). Assume that the weight of a person of average build varies directl as the cube of that person s height. The equation of variation has the form w kh. The weight that a person s legs will support is proportional to the cross-sectional area of the leg bones. This area varies directl as the square of the person s height. The equation of variation has the form s kh. Answer each question.. For a person feet tall who weighs 00 pounds, find a value for k in the equation w kh.. Use our answer from Eercise to predict the weight of a person who is feet tall.. Find the value for k in the equation w kh for a bab who is 0 inches long and weighs pounds.. How does our answer to Eercise demonstrate that a bab is significantl fatter in proportion to its height than an adult?. For a person feet tall who weighs 00 pounds, find a value for k in the equation s kh.. For a bab who is 0 inches long and weighs pounds, find an infant value for k in the equation s kh.. According to the adult equation ou found (Eercise ), how much would an imaginar giant 0 feet tall weigh?. According to the adult equation for weight supported (Eercise ), how much weight could a 0-foot tall giant s legs actuall support? 9. What can ou conclude from Eercises and? Glencoe/McGraw-Hill 9 Glencoe Algebra

20 - Stud Guide and Intervention Slope-Intercept Form Slope-Intercept Form Slope-Intercept Form m b, where m is the given slope and b is the -intercept Eample Write an equation of the line whose slope is and whose -intercept is. m b Slope-intercept form Replace m with and b with. Eample Graph. riginal equation Subtract from each side. (0, ) Divide each side b. Simplif. (, ) The -intercept of is and the slope is. So graph the point (0, ). From this point, move up units and right units. Draw a line passing through both points. Eercises Write an equation of the line with the given slope and -intercept.. slope:, -intercept. slope:, -intercept. slope:, -intercept Write an equation of the line shown in each graph.... (0, ) (, 0) (, 0) (0, ) (, ) (0, ) Lesson - Graph each equation Glencoe/McGraw-Hill 9 Glencoe Algebra

21 - Model Real-World Data Eample Stud Guide and Intervention (continued) Slope-Intercept Form MEDIA Since 99, the number of cable TV sstems has decreased b an average rate of sstems per ear. There were 0,9 sstems in 99. a. Write a linear equation to find the average number of cable sstems in an ear after 99. The rate of change is sstems per ear. In the first ear, the number of sstems was 0,9. Let N the number of cable TV sstems. Let the number of ears after 99. An equation is N 0,9. b. Graph the equation. The graph of N 0,9 is a line that passes through the point at (0, 0,9) and has a slope of. c. Find the approimate number of cable TV sstems in 000. N 0,9 riginal equation N () 0,9 Replace with. N 0,0 Simplif. There were about 0,0 cable TV sstems in 000. Number of Cable TV Sstems Cable TV Sstems N 0,900 0,00 0,00 0,00 0,00 0 Years Since 99 Source: The World Almanac Eercises ENTERTAINMENT In 99,.% of all households with TV s in the U.S. subscribed to cable TV. Between 99 and 999, the percent increased b about 0.% each ear.. Write an equation to find the percent P of households that subscribed to cable TV for an ear between 99 and Graph the equation on the grid at the right.. Find the percent that subscribed to cable TV in 999. PPULATIN The population of the United States is projected to be 00 million b the ear 00. Between 00 and 00, the population is epected to increase b about. million per ear.. Write an equation to find the population P in an ear between 00 and 00.. Graph the equation on the grid at the right.. Find the population in 00. Percent of Households with TV Having Cable Percent 0 Years Since 99 Source: The World Almanac Population (millions) P Projected United States Population P Years Since 00 Source: The World Almanac Glencoe/McGraw-Hill 9 Glencoe Algebra

22 - Skills Practice Slope-Intercept Form Write an equation of the line with the given slope and -intercept.. slope:, -intercept:. slope:, -intercept:. slope:, -intercept:. slope:, -intercept:. slope:, -intercept:. slope:, -intercept: 9. slope:, -intercept:. slope: 0, -intercept: Write an equation of the line shown in each graph (0, ) (0, ) (, ) (, ) (0, ) (, ) Graph each equation.... Lesson - Write a linear equation in slope-intercept form to model each situation.. A video store charges $0 for a rental card plus $ per rental.. A Norfolk pine is inches tall and grows at a rate of. feet per ear.. A Cairn terrier weighs 0 pounds and is on a special diet to lose pounds per month.. An airplane at an altitude of 000 feet descends at a rate of 00 feet per mile. Glencoe/McGraw-Hill 9 Glencoe Algebra

23 - Practice Slope-Intercept Form Write an equation of the line with the given slope and -intercept.. slope:, -intercept:. slope:, -intercept:. slope:., -intercept:. slope:., -intercept:. Write an equation of the line shown in each graph.... (0, ) (0, ) (, 0) (, 0) (, 0) (0, ) Graph each equation Write a linear equation in slope-intercept form to model each situation.. A computer technician charges $ for a consultation plus $ per hour.. The population of Pine Bluff is 9 and is decreasing at the rate of per ear. WRITING For Eercises, use the following information. Carla has alread written 0 pages of a novel. She plans to write additional pages per month until she is finished.. Write an equation to find the total number of pages P written after an number of months m.. Graph the equation on the grid at the right.. Find the total number of pages written after months. Carla s Novel 0 m Months Glencoe/McGraw-Hill 9 Glencoe Algebra Pages Written P

24 - NAME DATE PERID Reading to Learn Mathematics Slope-Intercept Form Pre-Activit How is a -intercept related to a flat fee? Read the introduction to Lesson - at the top of page in our tetbook. What point on the graph shows that the flat fee is $.00? How does the rate of $0.0 per minute relate to the graph? Reading the Lesson. Fill in the boes with the correct words to describe what m and b represent. m b. What are the slope and -intercept of a vertical line? The slope is undefined, and there is no -intercept.. What are the slope and -intercept of a horizontal line? The slope is 0, and the -intercept is where it crosses the -ais.. Read the problem. Then answer each part of the eercise. A rub-throated hummingbird weighs about 0. gram at birth and gains weight at a rate of about 0. gram per da until full grown. a. Write a verbal equation to show how the words are related to finding the average weight of a rub-throated hummingbird at an given week. Use the words weight at birth, rate of growth, weight, and weeks after birth. Below the equation, fill in an values ou know and put a question mark under the items that ou do not know. Lesson - weight? rate of growth weeks after birth 0.? weight at birth 0. b. Define what variables to use for the unknown quantities. c. Use the variables ou defined and what ou know from the problem to write an equation. Helping You Remember. ne wa to remember something is to eplain it to another person. Write how ou would eplain to someone the process for using the -intercept and slope to graph a linear equation. Glencoe/McGraw-Hill 9 Glencoe Algebra

25 - Enrichment Relating Slope-Intercept Form and Standard Forms rise You have learned that slope can be defined in terms of or. run Another definition can be found from the standard from of a linear equation. Standard form is A B C, where A, B, and C are integers, A 0, and A and B are not both zero.. Solve A B C for. Your answer should be written in slope-intercept form.. Use the slope-intercept equation ou wrote in Eercise to write epressions for the slope and the -intercept in terms of A, B, and C. Use the epressions in Eercise above to find the slope and -intercept of each equation Glencoe/McGraw-Hill 9 Glencoe Algebra

26 - Stud Guide and Intervention Writing Equations in Slope-Intercept Form Write an Equation Given the Slope and ne Point Eample Eample Write an equation of a line that passes through (, ) with slope. The line has slope. To find the -intercept, replace m with and (, ) with (, ) in the slope-intercept form. Then solve for b. m b Slope-intercept form ( ) b m,, and b Multipl. b Add to each side. Therefore, the equation is. Eercises Write an equation of the line that passes through (, ) with slope. The line has slope. Replace m with and (, ) with (, ) in the slope-intercept form. m b Slope-intercept form ( ) b m,, and b Multipl. b Add to each side. Therefore, the equation is. Write an equation of the line that passes through each point with the given slope.... (, ) m (, ) m m (0, 0). (, ), m. (, ), m. (, ), m. (, ), m 0. (, ), m 9. (, ), m Lesson - 0. Write an equation of a line that passes through the -intercept with slope.. Write an equation of a line that passes through the -intercept with slope.. Write an equation of a line that passes through the point (0, 0) with slope. Glencoe/McGraw-Hill 99 Glencoe Algebra

27 - Write an Equation Given Two Points Eample Stud Guide and Intervention (continued) Writing Equations in Slope-Intercept Form Write an equation of the line that passes through (, ) and (, ). Find the slope m. To find the -intercept, replace m with its computed value and (, ) with (, ) in the slope-intercept form. Then solve for b. m Slope formula m,,, m Simplif. m b Slope-intercept form () b Replace m with, with, and with. b Multipl. b Add to each side. Therefore, the equation is. Eercises Write an equation of the line that passes through each pair of points.... (, ) (0, ) (0, ) (, 0) (0, ) (, 0). (, ), (, 0). (0, ), (, ). (, ), (, ). (, ), (, ). (0, ), (, ) 9. (, ), (, ) 0. Write an equation of a line that passes through the -intercept and -intercept.. Write an equation of a line that passes through the -intercept and -intercept.. Write an equation of a line that passes through (0, ) and ( 0, 0). Glencoe/McGraw-Hill 00 Glencoe Algebra

28 - Skills Practice Writing Equations in Slope-Intercept Form Write an equation of the line that passes through each point with the given slope.... (, ) (, ) m m m (, ). (, 9), m. (, ), m. (, ), m. (, 0), m. (, ), m 9. (, ), m Write an equation of the line that passes through each pair of points (, ) (, ) (, ) (, ) (0, ) (, ). (, ), (, ). (, ), (, ). (, ), (, ). (, ), (0, ). (, ), (, ). (, ), (, ) Write an equation of the line that has each pair of intercepts. 9. -intercept:, -intercept: 0. -intercept:, -intercept: Lesson -. -intercept:, -intercept:. -intercept:, -intercept:. -intercept:, -intercept:. -intercept:, -intercept: Glencoe/McGraw-Hill 0 Glencoe Algebra

29 - Practice Writing Equations in Slope-Intercept Form Write an equation of the line that passes through each point with the given slope.... (, ) (, ) m m m (, ). (, ), m. (, ), m. (, ), m Write an equation of the line that passes through each pair of points (, ) (, ) (0, ) (, ) (, ) (, ) 0. (0, ), (, ). (, ), (, 0). (, ), (, ). (0, ), (, ). (, 0), (, ). (, 0), (, ) Write an equation of the line that has each pair of intercepts.. -intercept:, -intercept:. -intercept:, -intercept: 0. -intercept:, -intercept: 9. -intercept:, -intercept: 0. DANCE LESSNS The cost for dance lessons is $. The cost for lessons is $. Write a linear equation to find the total cost C for lessons. Then use the equation to find the cost of lessons.. WEATHER It is F at the 000-foot level of a mountain, and 9 F at the,000-foot level of the mountain. Write a linear equation to find the temperature T at an elevation e on the mountain, where e is in thousands of feet. Glencoe/McGraw-Hill 0 Glencoe Algebra

30 - NAME DATE PERID Reading to Learn Mathematics Writing Equations in Slope-Intercept Form Pre-Activit How can slope-intercept form be used to make predictions? Read the introduction to Lesson - at the top of page 0 in our tetbook. What is the rate of change per ear? about 000 per ear Stud the pattern on the graph. How would ou find the population in 99? Add 000 to the 99 population, which gives 9,000. Reading the Lesson. Suppose ou are given that a line goes through (, ) and has a slope of. Use this information to complete the following equation. m b b. What must ou first do if ou are not given the slope in the problem? Use the information given (two points) to find the slope.. What is the first step in answering an standardized test practice question? Read the problem.. What are four steps ou can use in solving a word problem? Eplore, Plan, Solve, Eamine. Define the term linear etrapolation. Linear etrapolation means using a linear equation to predict values that are outside the two given data points. Helping You Remember. In our own words, eplain how ou would answer a question that asks ou to write the slope-intercept form of an equation. Sample answer: Determine what information ou are given. If ou have a point and the slope, ou can substitute the - and -values and the slope into m b to find the value of b. Then use the values of m and b to write the equation. If ou have two points, use them to find the slope, and then use the method for a point and the slope. Lesson - Glencoe/McGraw-Hill 0 Glencoe Algebra

31 - NAME DATE PERID Enrichment Celsius and Kelvin Temperatures If ou blow up a balloon and put it in the refrigerator, the balloon will shrink as the temperature of the air in the balloon decreases. The volume of a certain gas is measured at 0 Celsius. The temperature is decreased and the volume is measured again. Temperature (t ) Volume (V ) 0 C 0 ml C 9 ml 0 C ml C ml C ml. Graph this table on the coordinate plane provided below. 00 V(mL) t ( C). Find the equation of the line that passes through the points ou graphed in Eercise. v t. Use the equation ou found in Eercise to find the temperature that would give a volume of zero. This temperature is the lowest one possible and is called absolute zero. C. In, Lord Kelvin proposed a new temperature scale with 0 being assigned to absolute zero. The size of the degree chosen was the same size as the Celsius degree. Change each of the Celsius temperatures in the table above to degrees Kelvin. 0, 9,,, Glencoe/McGraw-Hill 0 Glencoe Algebra

32 - Stud Guide and Intervention Writing Equations in Point-Slope Form Point-Slope Form Point-Slope Form m( ), where (, ) is a given point on a nonvertical line and m is the slope of the line Eample Eample Write the point-slope form of an equation for a line that passes through (, ) and has a slope of. m( ) Point-slope form ( ) m ; (, ) (, ) Therefore, the equation is ( ). Write the point-slope form of an equation for a horizontal line that passes through (, ). m( ) Point-slope form ( ) 0( ) 0 Simplif. Therefore, the equation is 0. m 0; (, ) (, ) Eercises Write the point-slope form of an equation for a line that passes through each point with the given slope.... (, ) m 0 m (, ) m (, ). (, ), m. (, ), m. (, ), m. (, ), m 0. (, 9), m 9. (, ), m 0. Write the point-slope form of an equation for the horizontal line that passes through (, ).. Write the point-slope form of an equation for the horizontal line that passes through (, ).. Write the point-slope form of an equation for the horizontal line that passes through (, 0). Lesson - Glencoe/McGraw-Hill 0 Glencoe Algebra

33 - Stud Guide and Intervention (continued) Writing Equations in Point-Slope Form Forms of Linear Equations Slope-Intercept Form Point-Slope Form m b m( ) m slope; b -intercept m slope; (, ) is a given point. Standard A B C A and B are not both zero. Usuall A is nonnegative and A, B, and C Form are integers whose greatest common factor is. Eample Eample Write ( ) in Write ( ) standard form. in slope-intercept form. ( ) riginal equation ( ) riginal equation ( ) ( ) Multipl each side b. Distributive Propert ( ) Distributive Propert Add to each side. Distributive Propert Subtract from each side. Therefore, the slope-intercept form of the Add to each side. Multipl each side b. equation is. Therefore, the standard form of the equation is. Eercises Write each equation in standard form.. ( ). ( ). ( 9). ( ). ( ). ( ) Write each equation in slope-intercept form.. ( ). ( ) 9. ( ) 0.. ( ). ( ) Glencoe/McGraw-Hill 0 Glencoe Algebra

34 - Skills Practice Writing Equations in Point-Slope Form Write the point-slope form of an equation for a line that passes through each point with the given slope.... m m (, ) (, ) m 0 (, ). (, ), m 0. (, ), m. (, ), m. (, ), m. (, ), m 9. (, ), m Write each equation in standard form ( ). ( ). ( ). ( ). ( ). 0 ( ). ( ). ( ) Write each equation in slope-intercept form. 9. ( ) 0. ( ). ( ). ( ). ( ). ( ). ( ). ( 9). Lesson - Glencoe/McGraw-Hill 0 Glencoe Algebra

35 - Practice Writing Equations in Point-Slope Form Write the point-slope form of an equation for a line that passes through each point with the given slope.. (, ), m. (, ), m. (, ), m 0. (, ), m. (, ), m. (, ), m Write each equation in standard form.. ( ). 0 ( ) 9. ( ) 0. ( ). ( ). ( )..( )..( )..( ) Write each equation in slope-intercept form.. ( ). ( ). ( ) 9. ( ) 0.. CNSTRUCTIN For Eercises, use the following information. A construction compan charges $ per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $9.. Write the point-slope form of an equation to find the total fee for an number of hours.. Write the equation in slope-intercept form.. What is the fee for the use of a trash dumpster? MVING For Eercises, use the following information. There is a set dail fee for renting a moving truck, plus a charge of $0.0 per mile driven. It costs $ to rent the truck on a da when it is driven miles.. Write the point-slope form of an equation to find the total charge for an number of miles for a one-da rental.. Write the equation in slope-intercept form.. What is the dail fee? Glencoe/McGraw-Hill 0 Glencoe Algebra

36 - NAME DATE PERID Reading to Learn Mathematics Writing Equations in Point-Slope Form Pre-Activit How can ou use the slope formula to write an equation of a line? Read the introduction to Lesson - at the top of page in our tetbook. Note that in the final equation there is a value subtracted from and from. What are these values? The value subtracted from is the -coordinate of the given point. The value subtracted from is the -coordinate of the given point. Reading the Lesson. In the formula m( ), what do and represent? and represent the coordinates of an given point on the graph of the line.. Complete the chart below b listing three forms of equations. Then write the formula for each form. Finall, write three eamples of equations in those forms. Sample eamples are given. Form of Equation Formula Eample slope-intercept m b point-slope m( ) ( ) standard A B C. Refer to Eample on page of our tetbook. What do ou think the hpotenuse of a right triangle is? Sample answers: The hpotenuse is the longest side of the right triangle. The hpotenuse is the side opposite the right angle in a right triangle. Helping You Remember. Suppose ou could not remember all three formulas listed in the table above. Which of the forms would ou concentrate on for writing linear equations? Eplain wh ou chose that form. Sample answer: Point-slope form; the slope-intercept form can be written from the point-slope form. This is so because the -intercept lets ou write the coordinates of the point where the line crosses the -ais. You can use that point as the given point in the point-slope formula. Lesson - Glencoe/McGraw-Hill 09 Glencoe Algebra

37 - Enrichment Collinearit You have learned how to find the slope between two points on a line. Does it matter which two points ou use? How does our choice of points affect the slope-intercept form of the equation of the line?. Choose three different pairs of points from the graph at the right. Write the slope-intercept form of the line using each pair.. How are the equations related?. What conclusion can ou draw from our answers to Eercises and? When points are contained in the same line, the are said to be collinear. Even though points ma look like the form a straight line when connected, it does not mean that the actuall do. B checking pairs of points on a line ou can determine whether the line represents a linear relationship.. Choose several pairs of points from the graph at the right and write the slope-intercept form of the line using each pair.. What conclusion can ou draw from our equations in Eercise? Is this a straight line? Glencoe/McGraw-Hill 0 Glencoe Algebra

38 - Stud Guide and Intervention Geometr: Parallel and Perpendicular Lines Parallel Lines Two nonvertical lines are parallel if the have the same slope. All vertical lines are parallel. Eample Write the slope-intercept form for an equation of the line that passes through (, ) and is parallel to the graph of. A line parallel to has the same slope,. Replace m with and (, ) with (, ) in the point-slope form. m( ) Point-slope form ( ( )) m ; (, ) (, ) ( ) Simplif. Distributive Propert Slope-intercept form Therefore, the equation is. Lesson - Eercises Write the slope-intercept form for an equation of the line that passes through the given point and is parallel to the graph of each equation.... (, ) (, ) (, ). (, ),. (, ),. (, ),. (, ), 0. (, ), 9. (, ), 0. Find an equation of the line that has a -intercept of that is parallel to the graph of the line.. Find an equation of the line that has a -intercept of that is parallel to the graph of the line.. Find an equation of the line that has a -intercept of that is parallel to the graph of the line. Glencoe/McGraw-Hill Glencoe Algebra

39 - Stud Guide and Intervention (continued) Geometr: Parallel and Perpendicular Lines Perpendicular Lines Two lines are perpendicular if their slopes are negative reciprocals of each other. Vertical and horizontal lines are perpendicular. Eample Write the slope-intercept form for an equation that passes through (, ) and is perpendicular to the graph of 9. Find the slope of 9. 9 riginal equation 9 Divide each side b. Subtract from each side. The slope of is. So, the slope of the line passing through (, ) that is perpendicular to this line is the negative reciprocal of, or. Use the point-slope form to find the equation. m( ) Point-slope form ( ( )) m ; (, ) (, ) ( ) Simplif. Distributive Propert Slope-intercept form Eercises Write the slope-intercept form for an equation of the line that passes through the given point and is perpendicular to the graph of each equation.. (, ),. (, ),. (, ),. (, ),. (, ),. (, ),. ( 9, ),. (, ), 9. (, ), 0. Find an equation of the line that has a -intercept of and is perpendicular to the graph of the line.. Find an equation of the line that has a -intercept of and is perpendicular to the graph of the line. Glencoe/McGraw-Hill Glencoe Algebra

40 - Skills Practice Geometr: Parallel and Perpendicular Lines Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of each equation.... (, ) (, ) (, ) Lesson -. (, ),. (, ),. (, ),. (, ),. (, ), 9. (, ), 0. (, ),. (, ),. (, ), 9 Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of each equation.. (, ),. (, ),. (, ),. (, ),. (, ),. (0, 0), 9. (, ), 0. (, ),. (0, ),. (, ), 0. (, ), 9. (, ), Glencoe/McGraw-Hill Glencoe Algebra

41 - Practice Geometr: Parallel and Perpendicular Lines Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of each equation.. (, ),. (, ),. (, ),. (, ),. (, ),. (, ),. (, ),. (, ), 9. (, ), 0. (, ), 9. (, ),. (, ), Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the graph of each equation.. (, ), 9. (, ),. (, ),. (0, ),. (, ),. (, ), 9. (, ), 0. (0, ),. (, ), 0. (, ),. (, ),. (, ), 9. GEMETRY Quadrilateral ABCD has diagonals A C and B D. Determine whether A C is perpendicular to B D. Eplain. A D B. GEMETRY Triangle ABC has vertices A(0, ), B(, ), and C(, ). Determine whether triangle ABC is a right triangle. Eplain. C Glencoe/McGraw-Hill Glencoe Algebra

42 - NAME DATE PERID Reading to Learn Mathematics Geometr: Parallel and Perpendicular Lines Pre-Activit How can ou determine whether two lines are parallel? Read the introduction to Lesson - at the top of page 9 in our tetbook. What is a famil of graphs? A group of graphs that have at least one characteristic in common, such as slope or -intercept. Lesson - Do ou think lines that do not appear to intersect are parallel or perpendicular? parallel Reading the Lesson. Refer to the Ke Concept bo on page 9. Wh does the definition use the term nonvertical when talking about lines with the same slope? Vertical lines have slopes that are undefined so we cannot sa the have the same slope.. What is a right angle? Sample answers: A right angle is one that measures 90. It is an angle formed b perpendicular lines.. Refer to the Ke Concept bo on page 9. Describe how ou find the opposite reciprocal of a number. Sample answer: The reciprocal of a given number is the number formed when ou switch the numerator and denominator. Then ou give it the opposite sign of the original number.. Write the opposite reciprocal of each number. a. b. c. d. Helping You Remember. ne wa to remember how slopes of parallel lines are related is to sa same direction, same slope. Tr to think of a phrase to help ou remember that perpendicular lines have slopes that are opposite reciprocals. Sample answer: Nicel right angles formed, use opposite reciprocals. Glencoe/McGraw-Hill Glencoe Algebra

43 - Enrichment Pencils of Lines All of the lines that pass through a single point in the same plane are called a pencil of lines. All lines with the same slope, but different intercepts, are also called a pencil, a pencil of parallel lines. Graph some of the lines in each pencil.. A pencil of lines through the. A pencil of lines described b point (, ) m( ), where m is an real number. A pencil of lines parallel to the line. A pencil of lines described b m m Glencoe/McGraw-Hill Glencoe Algebra

44 - Stud Guide and Intervention Scatter Plots and Lines of Fit Interpret Points on a Scatter Plot A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. If increases as increases, there is a positive correlation between and. If decreases as increases, there is a negative correlation between and. If and are not related, there is no correlation. Eample EARNINGS The graph at the right shows the amount of mone Carmen earned each week and the amount she deposited in her savings account that same week. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. The graph shows a positive correlation. The more Carmen earns, the more she saves. Eercises Carmen s Earnings and Savings 0 Dollars Saved Dollars Earned Lesson - Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive correlation, describe it... Average Weekl Work Hours in U.S. Hours.... Average Jogging Speed Miles per Hour Years Since Minutes Source: The World Almanac.. Growth of Investment Clubs Number of Clubs (thousands) 0 Years Since 990 Source: The Wall Street Journal Almanac Number of Mutual Funds Number of Funds (thousands) 0 Years Since 99 Source: The Wall Street Journal Almanac Glencoe/McGraw-Hill Glencoe Algebra

45 - Lines of Fit Eample The table below shows the number of students per computer in United States public schools for certain school ears from 990 to 000. Year Students per Computer 0.. a. Draw a scatter plot and determine what relationship eists, if an. Since decreases as increases, the correlation is negative. b. Draw a line of fit for the scatter plot. Draw a line that passes close to most of the points. A line of fit is shown. c. Write the slope-intercept form of an equation for the line of fit. The line of fit shown passes through (99, ) and (999,.). Find the slope.. m m. Find b in. b.. 99 b 0 b Therefore, an equation of a line of fit is. 0. Eercises Stud Guide and Intervention (continued) Scatter Plots and Lines of Fit Refer to the table for Eercises. Years Hourl. Draw a scatter plot.. Write the slope-intercept Since 99 Wage form of an equation for the. Draw a line of fit for the data. line of fit. 0 $. U.S. Production $. Workers Hourl Wage $. $. $. Hourl Wage (dollars) 0 Years Since 99 Source: The World Almanac Students per Computer 0 0 Students per Computer in U.S. Public Schools Year Source: The World Almanac Glencoe/McGraw-Hill Glencoe Algebra

46 - Skills Practice Statistics: Scatter Plots and Lines of Fit Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.. Calories Burned. During Eercise Calories Time (minutes) Fines (dollars) Librar Fines 0 0 Books Borrowed Lesson -.. Weight-Lifting Repetitions Weight (pounds) Number of Newspapers Evening Newspapers Year Source: Editor & Publisher BASEBALL For Eercises, use the scatter plot that shows the average price of a major-league baseball ticket from 99 to Determine what relationship, if an, eists in the data. Eplain.. Use the points (99, 9.0) and (99,.0) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot. Average Price ($) 0 0 Baseball Ticket Prices Year. Predict the price of a ticket in 00. Source: Team Marketing Report, Chicago Glencoe/McGraw-Hill 9 Glencoe Algebra

47 - Practice Statistics: Scatter Plots and Lines of Fit Determine whether each graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation... Temperature versus Rainfall Average Temperature ( F) Average Annual Rainfall (inches) Source: National ceanic and Atmospheric Administration Highest Point (thousands of feet) State Elevations Mean Elevation (feet) Source: U.S. Geological Surve DISEASE For Eercises, use the table that shows the number of cases of mumps in the United States for the ears 99 to Draw a scatter plot and determine what relationship, if an, eists in the data.. Draw a line of fit for the scatter plot.. Write the slope-intercept form of an equation for the line of fit.. Predict the number of cases in 00. ZS For Eercises 0, use the table that shows the average and maimum longevit of various animals in captivit.. Draw a scatter plot and determine what relationship, if an, eists in the data. U.S. Mumps Cases Year Cases 90 Source: Centers for Disease Control and Prevention U.S. Mumps Cases Cases Year Longevit (ears) Avg. 0 0 Ma Source: Walker s Mammals of the World. Draw a line of fit for the scatter plot. 9. Write the slope-intercept form of an equation for the line of fit. 0. Predict the maimum longevit for an animal with an average longevit of ears. Glencoe/McGraw-Hill 0 Glencoe Algebra

48 - NAME DATE PERID Reading to Learn Mathematics Statistics: Scatter Plots and Lines of Fit Pre-Activit How do scatter plots help identif trends in data? Read the introduction to Lesson - at the top of page 9 in our tetbook. What does the phrase linear relationship mean to ou? Sample answer: It means that when ou graph the data points on a coordinate grid, the points all lie on or close to a line that ou could draw on the grid. Write three ordered pairs that fit the description as increases, decreases. Sample answer: {(, ), (, ), (, )} Lesson - Reading the Lesson. Look up the word scatter in a dictionar. How does this definition compare to the term scatter plot? ne definition states to occur or fall irregularl or at random. The points in a scatter plots usuall do not follow an eact linear pattern, but fall irregularl on the coordinate plane.. What is a line of fit? How man data points fall on the line of fit? A line of fit shows the trend of the data. It is impossible to sa how man data points ma fall on a line of fit mabe several, mabe none.. What is linear interpolation? How can ou distinguish it from linear etrapolation? Linear interpolation is the process of predicting a -value for a given -value that lies between the least and greatest -values in the data set. Inter- means between and etra- means beond. If the -value is between the etremes of the -values in the data set, ou sa interpolation; if the -value is less than or greater than the etremes, ou sa etrapolation. Helping You Remember. How can ou remember whether a set of data points shows a positive correlation or a negative correlation? If it looks like a line of fit for the points would have a positive slope, there is a positive correlation. If it looks like a line of fit would have a negative slope, there is a negative correlation. Glencoe/McGraw-Hill Glencoe Algebra

49 - Enrichment Latitude and Temperature The latitude of a place on Earth is the measure of its distance from the equator. What do ou think is the relationship between a cit s latitude and its Januar temperature? At the right is a table containing the latitudes and Januar mean temperatures for fifteen U.S. cities. U.S. Cit Latitude Januar Mean Temperature Alban, New York :0 N 0. F Albuquerque, New Meico :0 N. F Anchorage, Alaska : N.9 F Birmingham, Alabama : N. F Charleston, South Carolina : N. F Chicago, Illinois :0 N.0 F Columbus, hio 9:9 N. F Duluth, Minnesota : N.0 F Fairbanks, Alaska :0 N 0. F Galveston, Teas 9: N.9 F Honolulu, Hawaii :9 N.9 F Las Vegas, Nevada : N. F Miami, Florida : N. F Richmond, Virginia : N. F Tucson, Arizona : N. F Sources: and Use the information in the table to create a scatter plot and draw a line of best fit for the data.. Write an equation for the line of fit. Make a conjecture about the relationship between a cit s latitude and its mean Januar temperature.. Use our equation to predict the Januar mean temperature of Juneau, Alaska, which has latitude : N. Temperature ( F) T Latitude ( N) L. What would ou epect to be the latitude of a cit with a Januar mean temperature of F?. Was our conjecture about the relationship between latitude and temperature correct?. Research the latitudes and temperatures for cities in the southern hemisphere instead. Does our conjecture hold for these cities as well? Glencoe/McGraw-Hill Glencoe Algebra

50 NAME DATE PERID Chapter Test, Form SCRE Write the letter for the correct answer in the blank at the right of each question. For Questions, find the slope of each line described.. the line through (, ) and (, ) A. B. C. D... the line through (, ) and (, ) A. 9 B. C. 0 D. undefined.. the line graphed at the right A. B. C. D. (0, ). (, ). a vertical line A. B. 0 C. D. undefined.. Which graph has a slope of? A. B. C. D.. Assessment. CMMUNICATIN In 99, there were area codes in the United States. In 999, there were. Find the rate of change from 99 to 999. A. B. C. D.. For Questions 9, find the equation in slope-intercept form that describes each line.. a line through (, ) with slope 0 A. B. C. D... a line through (, ) with slope A. B. C. 0 D.. 9. a line through (, ) and (, ) A. B. C. D If deli sandwiches cost $9., how much will sandwiches cost? A. $. B. $9. C. $.0 D. $ What is the standard form of ( )? A. B. C. D.. Glencoe/McGraw-Hill Glencoe Algebra

51 NAME DATE PERID Chapter Test, Form (continued). Which is the graph of? A. B. C. D... Which is the point-slope form of an equation for the line that passes through (0, ) with slope? A. B. C. D. ( ).. What is the slope-intercept form of ( )? A. B. C. D... When are two lines parallel? A. when the slopes are opposite B. when the slopes are equal C. when the product of the slopes is D. when the slopes are positive.. Find the slope-intercept form of an equation for the line that passes through (, ) and is parallel to. A. B. 0. C. D Find the slope-intercept form of an equation of the line perpendicular to the graph of and passing through (0, ). A. B. C. D.. For Questions and 9, use the scatter plot at the right.. How would ou describe the relationship between 90 the and values in the scatter plot? 0 A. strong negative correlation 0 0 B. weak negative correlation 0 C. weak positive correlation 0 '0 ' '90 '9 '00 D. strong positive correlation. 9. Based on the data in the scatter plot, what would ou epect the value to be for 00? A. greater than 0 B. between 0 and C. between and 0 D. less than What is an equation of the line whose graph has slope of and a -intercept of? A. B. C. D. 0. Bonus Find the value of r in (, r), (r, ) so that the slope of the line containing them is. B: Glencoe/McGraw-Hill Glencoe Algebra

52 NAME DATE PERID Chapter Test, Form A SCRE Write the letter for the correct answer in the blank at the right of each question.. What is the slope of the line through (, 9) and (, )? A. B. C. D... What is the slope of the line through (, ) and (, )? A. 0 B. undefined C. 9 D... Find the value of r so that the line through (, r) and (, ) has a slope of. A. B. C. D... In 99, there were,000 students at Beacon High. In 000, there were,0. What is the rate of change in the number of students? A. 0/r B. 0/r C. /r D. 00/r.. Which is the graph of? A. B. C. D... If varies directl as and when 0, find when. A. 0 B. C. D. none of these. Assessment. A driver s distance varies directl as the amount of time traveled. After hours, a driver had traveled 90 miles. How far had the driver traveled after hours? A. 0 miles B. 0 miles C. 0 miles D. 0 miles.. A line of fit might be defined as A. a line that connects all the data points. B. a line that might best estimate the data and be used for predicting values. C. a vertical line halfwa through the data. D. a line whose slope is greater than.. 9. What is the slope-intercept form of the equation of a line with slope and -intercept? A. B. C. D Which equation is graphed at the right? A. 0 B. C. D. 0.. Which is an equation of the line that passes through (, ) and (, )? A. B. C. D. 9. Glencoe/McGraw-Hill Glencoe Algebra

53 NAME DATE PERID Chapter Test, Form A (continued). What is the standard form of the equation of the line through (0, ) with slope? A. B. C. D... Which is an equation of the line with slope and a -intercept of? A. ( ) B. C. D... What is the standard form of ( )? A. B. C. 9 D... What is the equation of the line through (, ) with a slope of 0? A. B. C. 0 D. 0.. Find the slope-intercept form of the equation of the line that passes through (, ) and is parallel to 0. A. B. C. D... If line q has a slope of, what is the slope of an line perpendicular to q? A. B. C. D.. For Questions and 9, use the scatter plot at the right.. Which data are shown b the scatter plot? A. (90,.), (9,.), (99,.) B. (90,.), (9,.), (99,.) C. (90,.), (9,.), (990,.0) D. (90,.), (9,.), (990,.0) '0 ' ' Based on the data in the scatter plot, what would ou epect the value to be for 99? A. between and B. higher than C. between and D. impossible to tell To calculate the charge for a load of bricks, including deliver, the Redstone Brick Co. uses the equation C 0.b, where C is the charge and b is the number of bricks. What is the deliver fee per load? A. $ B. $ C. $ D. It depends on the number of bricks 0. Bonus What is the -intercept of a line through (, ) and perpendicular to the line? B: 0 Glencoe/McGraw-Hill Glencoe Algebra

54 NAME DATE PERID Chapter Test, Form B SCRE Write the letter for the correct answer in the blank at the right of each question.. What is the slope of the line through (, ) and (, )? A. 9 B. C. D. 9.. What is the slope of the line through (, ) and (9, )? A. B. C. 0 D. undefined.. Find the value of r so that the line through (, ) and (, r) has a slope of. A. B. C. D... In 99, MusicMart sold,000 CDs. In 000, the sold,0 CDs. What is the rate of change in the number of CDs sold? A. 0/r B. 0/r C. /r D. 00/r.. Which is the graph of? A. B. C. D... If varies directl as and when, find when 9. A. B. C. 0 D.. 9 Assessment. The amount a spring stretches varies directl as the weight of the object attached to it. If an -ounce weight stretches a spring 0 centimeters, how much weight will stretch it centimeters? A. oz B. oz C. 0 oz D. oz.. The graph of data that has a strong negative correlation has A. a narrow linear pattern from lower left to upper right. B. a narrow linear pattern from upper left to lower right. C. a narrow horizontal pattern below the -ais. D. all negative -values.. 9. What is the slope-intercept form of the equation of the line with slope and -intercept at the origin? A. B. C. D Which equation is graphed at the right? A. B. C. D. 0.. Which is an equation of the line that passes through (, ) and (, 9)? A. B. C. D.. Glencoe/McGraw-Hill Glencoe Algebra

55 NAME DATE PERID Chapter Test, Form B (continued). What is the standard form of the equation of the line through (, ) with slope? A. B. C. D... Which is an equation of the line with slope that passes through (, )? A. ( ) B. C. ( ) D. ( ).. What is the standard form of ( )? A. 0 B. C. 0 D. 0.. What is the equation of the line through (, ) with an undefined slope? A. B. C. 0 D. 0.. Find the slope-intercept form of the equation of the line that passes through (, ) and is parallel to. A. 9 B. 9 C. 9 D... If line q has a slope of, what is the slope of an line perpendicular to q? A. B. C. D.. For Questions and 9, use the scatter plot at the right.. Which data are shown b the scatter plot? A. (90, ), (90, ), (9, ) B. (90, 0), (9, ), (990, 0) C. (, 90), (, 90), (, 9) D. (9, ), (90, ), (9, ). 9. Based on the data in the scatter plot, which statement is true? A. As increases, increases. B. As increases, decreases. C. There is no relationship between and. D. There are not enough data to determine the relationship between and A bab blue whale weighed tons at birth. Ten das later, it weighed tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d das old? A. w 0d B. w 0d C. w 0.d D. w d 0 0. Bonus For what value of k does k 0 have a slope of? B: 0 0 '0 '0 '90 Glencoe/McGraw-Hill Glencoe Algebra

56 NAME DATE PERID Chapter Test, Form C SCRE For Questions, find the slope of the line passing through each pair of points. If the slope is undefined, write undefined.. (, ) and (, ).. (, ) and (, ).. (, ) and (, ).. Find the value of r so that the line through (, ) and. (r, ) has a slope of.. In 9, vehicle emission standards allowed.. hdrocarbons released per mile driven. B 90, the standards allowed onl 0. hdrocarbons per mile driven. What was the rate of change from 9 to 90?. Graph.. Assessment. If a shark can swim miles in 9 hours, how man miles. will it swim in hours?. Write a linear equation in slope-intercept form to model the. situation: A telephone compan charges $. per month plus 0 a minute for long-distance calls. 9. Write an equation in standard form of the line that passes 9. through (, ) and has a -intercept of. 0. Write the slope-intercept form of an 0. equation for the line graphed at the right.. Graph the line with -intercept and. slope. Glencoe/McGraw-Hill 9 Glencoe Algebra

57 NAME DATE PERID Chapter Test, Form C (continued). Write an equation in slope-intercept form for the line that. passes through (, ) and (, ).. Write an equation in standard form for the line whose slope. is undefined and passes through (, ).. Write an equation in point-slope form for the line that has. slope and passes through (, ).. Write the standard form of the equation ( )... Write the slope-intercept form of the equation. ( ).. Write the slope-intercept form of the equation of the line. parallel to the graph of that passes through (0, ).. Write the slope-intercept form of the equation of the line. perpendicular to the graph of that passes through (, ). For Questions 9 and 0, use the data in the table. Time Spent Studing (min) Score Received (percent) 9 9. Make a scatter plot relating time spent studing to the 9. score received. Score Received (percent) Write the slope-intercept form of the equation for a line 0. of fit for the data. Use our equation to predict a student s score if the student spent minutes studing. Bonus In a certain lake, a -ear-old bluegill fish is inches B: long, while a -ear-old bluegill fish is. inches long. Assuming the growth rate can be approimated b a linear equation, write an equation in slope-intercept form for the length of a bluegill fish in inches after t ears. Then use the equation to determine the age of a 9-inch bluegill Time Spent Studing (minutes) Glencoe/McGraw-Hill 0 Glencoe Algebra

58 NAME DATE PERID Chapter Test, Form D SCRE For Questions, find the slope of the line passing through each pair of points. If the slope is undefined, write undefined.. (, ) and (, ).. (, ) and (, ).. (, ) and (, ).. Find the value of r so that the line through (, ) and. (r, ) has a slope of.. In 9,.% of college students graduated in or fewer. ears of stud. In 99, that number had fallen to.%. What was the change of rate for percent of students graduating within ears from 9 to 99?. Graph.. Assessment. If a snail travels 00 inches in hours, how long will it take. the snail to travel 0 inches?. Write a linear equation in slope-intercept form to model. the situation: An Internet compan charges $.9 per month plus $.0 for each hour of use. 9. Write an equation in standard form of the line that passes 9. through (, ) and has a -intercept of. 0. Write the slope-intercept form 0. of an equation for the line graphed at the right.. Graph the line with -intercept. and slope. Glencoe/McGraw-Hill Glencoe Algebra

59 NAME DATE PERID Chapter Test, Form D (continued). Write an equation in slope-intercept form for the line that. passes through (, ) and (, ).. Write an equation in standard form for the line whose slope. is undefined that passes through (, ).. Write an equation in point-slope form for the line that has. slope and passes through (, 0).. Write the standard form of the equation ( )... Write the slope-intercept form of the equation. ( ).. Write the slope-intercept form of the equation of the line. parallel to the graph of 9 that passes through (, ).. Write the slope-intercept form of the equation of the line. perpendicular to the graph of that passes through (, ). For Questions 9 and 0, use the data that shows age and percent of budget spent on entertainment in the table. Age Percent Spent on Entertainment Make a scatter plot relating the age to the percent of the 9. person s budget spent on entertainment. Percent Spent on Entertainment Age 0. Write the slope-intercept form of the equation for a line 0. of fit for the data. Use our equation to predict the percent of a -ear-old person s budget. Bonus Write an equation in slope-intercept form of the line B: with -intercept and parallel to a line perpendicular to 0. Glencoe/McGraw-Hill Glencoe Algebra

60 NAME DATE PERID Chapter Test, Form SCRE For Questions and, find the slope of the line passing through each pair of points. If the slope is undefined, write undefined.. (, ) and (, ).. (, 9) and (, ).. Find the value of r so that the line through (, ) and (r, ). has a slope of.. Find the value of r so that the line through (r, ) and (, r). has a slope of.. In 990, there were approimatel,000 people in. Lancaster. Five ears later, the population was,. Find the rate of change in the population.. Graph.. Assessment. If an ostrich can run kilometers in minutes, how. man kilometers can it run in an hour?. Write the point-slope form of an equation of the line that has. slope and passes through (, ). 9. Write an equation in standard form of the line that passes 9. through (, ) and (, ). 0. Graph a line whose -intercept is and whose slope is. 0.. Write ( 9) in standard form... Write the point-slope form of the equation for the line that. has -intercept and -intercept. Glencoe/McGraw-Hill Glencoe Algebra

61 NAME DATE PERID Chapter Test, Form (continued) For Questions 0, write an equation in slope-intercept form of the line satisfing the given conditions.. has -intercept and slope.. has slope and passes through (, ).. passes through (, ) and (, ).. is horizontal and passes through (, ).. is parallel to the -ais and has an -intercept of.. is perpendicular to and passes through (, ). 9. is parallel to and passes through (0, ) is perpendicular to the -ais and passes through (, ) 0. For Questions, use the data in the table.. Make a scatter plot relating the verbal scores and the. math scores. State Graduation Scores Year Verbal Score Math Score Math Score Verbal Score. Does the scatter plot in Question show a positive, a. negative, or no correlation? What does that relationship represent?. Write the equation for a line of fit. Predict the. corresponding math score for a verbal score of.. A rental car compan charges $.99 per da, including 00. free kilometers. There is a charge of $0./km for additional kilometers. Write a linear equation that models this situation.. Write the slope-intercept form of 0.( 0).. Bonus The area of a circle varies directl as the square of the B: radius. If the radius is tripled, b what factor will the area increase? Glencoe/McGraw-Hill Glencoe Algebra

62 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 problem.. Draw a line on a coordinate plane so that ou can determine at least two points on the graph. a. Describe how ou would determine the slope of the graph and justif the slope ou found. b. Eplain how ou could use the slope to write various forms of the equation of that line. Then write three forms of the equation.. You are told that a line passes through (, ). a. Discuss what other information ou would need to graph this line. b. Then describe how ou would use that information to graph the line and write its equation.. Refer to the scatter plot at the right. a. Describe the pattern of points in the scatter plot and the relationship between and. b. Give at least two eamples of real-life situations that, if graphed, would result in a correlation like the one shown in this scatter plot. c. Add a scale and heading to each ais. Then write an equation that would model the points represented b this plot. Assessment. The table gives the life epectanc of a child born in the United States in a given ear. a. Make a scatter plot of the data. b. Can ou use the data to claim that the increase in life epectanc is due to improved health care? Eplain our response. c. Use the data to predict the life epectanc of a bab born in 000. Eplain how ou determined our answer. Years of Life Epected at Birth Year of Birth Life Epectanc (ears) Source: National Center for Health Statistics Glencoe/McGraw-Hill Glencoe Algebra

63 NAME DATE PERID Chapter Vocabular Test/Review SCRE best-fit line constant of variation direct variation famil of graphs linear etrapolation linear interpolation line of fit negative correlation parallel lines perpendicular lines point-slope form positive correlation rate of change scatter plot slope slope-intercept form standard form Choose from the terms above to complete each sentence.. If two lines have slopes that are negative reciprocals of each other, then the are. If the have slopes that are the same, then the are.. In the equation, k, k represents the.. A graph of data points is sometimes called a.. Several graphs who have one or more common characteristics form a.. Earning $.0 per hour is an eample of a.. The leftmost data point in a set is (, ) and the rightmost point is (, ). If ou use a linear prediction equation to find the corresponding value for 0, ou are using a method called.. The ratio of the rise to the run or the ratio of the change in the -coordinates to the change in the -coordinates are definitions of.. The equation is written in form. 9. The equation ( ) is written in form. 0. The equation is written in form. In our own words Define each term.. line of fit. linear etrapolation Glencoe/McGraw-Hill Glencoe Algebra

64 NAME DATE PERID Chapter Quiz (Lessons and ) SCRE Determine the slope of the line passing through each pair of points.. (, ) and (, ).. (9, ) and (, ).. (, 0) and (, ).. In 99, there were approimatel students in the. Delaware High School band. In 00, that number increased to 0. Find the annual rate of change in the number of students in the band.. Chris s wages var directl as the time she works. If her. wages for 0 hours are $0, what are her wages for hours? NAME DATE PERID Chapter Quiz (Lessons and ) SCRE Assessment Write the slope-intercept form of the equation for each situation.. slope:, -intercept:.. line passing through (9, ) and (, ).. Graph... Write a linear equation in slope-intercept form to model a tree feet tall that grows inches per ear... STANDARDIZED TEST PRACTICE The table of ordered pairs shows the coordinates of the two points on the graph of a function. Which equation describes the function? A. B. C. D.. Glencoe/McGraw-Hill Glencoe Algebra

65 NAME DATE PERID Chapter Quiz (Lessons and ) SCRE. Write the point-slope form of an equation for a line passing. through (, ) with slope m.. Write 9 ( ) in slope-intercept form... Write the point-slope form of an equation for the horizontal. line that passes through (, ).. Write the slope-intercept form of an equation for the line. that passes through (, ) and is parallel to.. Write the slope-intercept form of an equation for the line. that passes through (0, ) and is perpendicular to 9. NAME DATE PERID Chapter Quiz (Lesson ) SCRE. Use the data in the table to make a scatter plot relating. age to median income. Age 9 0 Median Income ($000) Draw a fit line for the scatter plot. Median Income ($000) Age. Do the data show a positive or negative relationship? What. does this relationship mean?. Write the slope-intercept form of an equation for a line of fit... Use the line of fit to predict the median income for someone. ears old. Glencoe/McGraw-Hill Glencoe Algebra

66 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.. Find the slope of the line through (, ) and (, ). A. B. C. D... Find the slope of the line through (0, ) and (, ). A. 0 B. C. D. no slope.. In 999, 9.0 quadrillion Btu (British thermal units) of energ were consumed in the United States. In 99, 90. quadrillion Btu were consumed. Which of the following is the rate of change in consumption from 99 to 999? A.. quadrillion btu per ear B.. quadrillion btu per ear C. 0.9 ears per quadrillion btu D. 0. quadrillion btu per ear.. The total price of a bag of peaches varies directl with the cost per pound. If pounds of peaches cost $.0, how much would. pounds cost? A. $.0 B. $.0 C. $.00 D. $.9.. Which is the slope-intercept form of an equation for the line containing (0, ) with slope? A. B. C. D.. Assessment Part II For Questions, write an equation in slope-intercept form of the line satisfing the given conditions.. has -intercept and slope.. passes through (, ) and (0, ).. has slope and passes through (, ). For Questions 9 and 0, use the graph at the right. 9. What is the slope of the line shown P(, 0) 9. in the graph? 0. What is the equation of the line 0. shown in the graph? Glencoe/McGraw-Hill 9 Glencoe Algebra

67 NAME DATE PERID Chapter Cumulative Review (Chapters ). Write r r s s using eponents. (Lesson -).. Evaluate if and. (Lesson -). Simplif each epression. (Lessons - through -) (.) (.) ( ) ( ). a b. For Questions 9, solve each equation. (Lessons - through -) 9. m Solve if the domain is {,, 0,, }.. (Lesson -). Determine whether {(, ), (, ), (, ), (, )} is a function,. and eplain our reasoning. (Lesson -). Write an equation for the relationship between the variables. in the chart. (Lesson -) 0. Determine the slope of the line passing through (, ) and. (, ). (Lesson -). Write an equation in slope-intercept form for the line. passing through (, ) with slope. (Lesson -). Write an equation for the line passing through (, ) and. (, ). (Lesson -). Write the slope-intercept form of an equation for the line. that is parallel to and passes through (0, ). (Lesson -) Glencoe/McGraw-Hill 0 Glencoe Algebra

68 NAME DATE PERID Standardized Test Practice (Chapters ) Part : Multiple Choice Instructions: Fill in the appropriate oval for the best answer.. If a, b, and c, then ( a b)? (Lesson -) b c A. B. 0. C. 0 D A B C D. If n, what is the value of n? (Lesson -) E. 0 F. G. H.. E F G H. Lnn has more books than José. If Lnn gives José of her books, how man more will José have than Lnn? (Lesson -) A. B. C. D. 0. A B C D. If, which value of does NT form a proportion? (Lesson -) E. F. G. H... Two-thirds of a number added to itself is 0. What is the number? (Lesson -) A. B. C. 0 D.. E A F B G C H D Assessment. % of 90 is 9.% of what number? (Lesson -) E.. F. G. 0 H. 00. E F G H. For what value(s) of r is r r? (Lesson -) A. all numbers B. all negative integers C. 0 D. no values of r. A B C D. The range of a relation includes the integers,, and. What could be a value for in the domain? (Lesson -) E. 0 F. 0 G. H. 0. E F G H 9. A line with a slope of passes through points at (, ) and (, ). Find the value of. (Lesson -) A. B. C. 0 D. 9. A B C D 0. If a line passes through (0, ) and has a slope of, what is an equation for the line? (Lesson -) E. F. G. H. 0. E F G H Glencoe/McGraw-Hill Glencoe Algebra

69 NAME DATE PERID Standardized Test Practice (continued) 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.. If and, what is the greatest.. possible value of ( )? (Lesson -). If,? (Lesson -). The formula for the volume of a rectangular.. solid is V Bh. A packing crate has a height / / of. inches and a base area of. square.... inches. What is the volume of the crate in cubic inches? (Lesson -) Find the slope of a line parallel to. (Lesson -) / / / /... / / Part : Quantitative Comparison Instructions: Compare the quantities in columns A and B. Shade in A if the quantit in column A is greater; B if the quantit in column B is greater; C if the quantities are equal; or D if the relationship cannot be determined from the information given. Column A Column B. n the number line above, the marks are equall spaced.. A B C D (Lesson -) A B C D (Lesson -) Glencoe/McGraw-Hill Glencoe Algebra

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