Chapter 5 Resource Masters

Transcription

1 Chapter Resource Masters

2 NAME DATE PERID 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

3 NAME DATE PERID 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

4 - Find Slope NAME DATE PERID 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 ( ) 7 7 Slope formula,,, Simplif. Find the value of r so that the line through (0, r) and (, ) has a slope of. 7 m Slope formula r 7 0 m 7,, r,, 0 r Simplif. 7 7 ( 7) 7( r) Cross multipl. 8 7r Distributive Propert 7r r Divide each side b 7. Subtract 8 from each side. Lesson - Eercises Find the slope of the line that passes through each pair of points.. (, 9), (, 6). (, ), (, ). (, ), (, ). (, ), (8, 9). (, 8), (7, 6) 6. (, ), (8, ) 7. (, ), (6, ) 8. (, ), (6, ) 9. (,.), (,.) Determine the value of r so the line that passes through each pair of points has the given slope. 0. (6, 8), (r, ), m. (, ), (7, r), m. (, 8), (r, ) m. (7, ), (6, r), m 0. (r, ),(7,),m. (7, ), (r, 9),m 6 6. (0, r), (, ), m 7. (0, ), (, r), m (r, ),(7,r), m 7 Glencoe/McGraw-Hill 8 Glencoe Algebra

5 - NAME DATE PERID 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 and for change in population : change in time change in population : change in time 0.8 or 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 97, the growth was 0.0 billion per ear, or. million per ear. From , 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 than for Therefore, the section of the graph for 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 8 Glencoe Algebra

6 - NAME DATE PERID Skills Practice Slope Find the slope of the line that passes through each pair of points.... (, ) (0, ) (0, ) (, ) (0, 0) (, ). (, ), (, 6). (6, ), ( 6, ) 6. (, 6), (, 8) 7. (, ), (, ) Lesson - 8. (, ), (, ) 9. (9, 8), (7, 8) 0. (, 8), ( 8, ). (, 0), (, 7). (7, 8), (8, 7). ( 6, ), (, ). (0, 0), (, ). (, ), ( 8, ) 6. (, 9), (, ) 7. (, 6), (, ) 8. (, ), ( 8, ) 9. (, 6), (7, 8) 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, ),(6,),m. (r, ),(7,),m. (, ), (r, ), m. (7, r), (, 6), m 0 Glencoe/McGraw-Hill 8 Glencoe Algebra

7 - NAME DATE PERID Practice Slope Find the slope of the line that passes through each pair of points.... (, ) (, ) (, ) (, ) (, 0) (, ). (6, ), (7, ). ( 9, ), ( 7, ) 6. (6, ), (, ) 7. (7, ), (, 8) 8. ( 7, 8), ( 7, ) 9. (, 9), (, 9) 0. (, ), ( 6, ). (, 9), (, 8). (, ), (7, 8). (, 0), (, ). (0., 0.9), (0., 0.9). 7,,, Find the value of r so the line that passes through each pair of points has the given slope. 6. (, r), (6, 7), m 7. (, ), (r, ),m (, ), (, r), m 9. (, r), (, ), m 6 0. (, ), (r, ),m undefined. ( 7, ), ( 8, r), m. (r, 7),(,8),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 8, 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 8 Glencoe Algebra

8 - 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 6 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 units Thus, the slope of this line is or. 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 run b. how far up or down as compared to how far left or right $,000 increase in spending 6 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 8 Glencoe Algebra

9 - NAME DATE PERID 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 86 Glencoe Algebra

10 - NAME DATE PERID 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. 6 k Divide each side b. Therefore, the equation is 6. b. Use the direct variation equation to find when 8. 6 Direct variation equation 8 6 Replace with 8. Divide each side b 6. Therefore, when 8. 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 6.. If 9 when, find when If.8 when.6, find when. 7. If when,find when 8 6. Glencoe/McGraw-Hill 87 Glencoe Algebra

11 - 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 60 miles. d t riginal equation 60 t Replace d with 60. t 8 Divide each side b. Therefore, it will take 8 hours to drive 60 miles. Eercises NAME DATE PERID Stud Guide and Intervention (continued) Slope and Direct Variation Distance (miles) d Automobile Trips d t (, ) 90 (, ) 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. 6. Find the volume of the same gas at 0 (absolute temperature). Volume (cubic feet) V Charles s Law T Temperature ( K) Glencoe/McGraw-Hill 88 Glencoe Algebra

12 - NAME DATE PERID 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. 7. If 8 when, find 8. If when, find when. when. Lesson - 9. If when, find 0. If 9 when, find when 6. when.. If when 6, find. If when 8, find when 6. when 6. 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 $.80 times the number of gallons g. is times the total number of crates c. Cost ($) C Gasoline Cost Tos T Tos Shipped g Gallons c Crates Glencoe/McGraw-Hill 89 Glencoe Algebra

13 - 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. 7. If 7. when 0., find when 0.. ;. 8. If 80 when, find when 00..; 0 9. If when, find when. ; 8 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; $.6 Glencoe/McGraw-Hill 90 Glencoe Algebra

14 - 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 6 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 6 gallons of water per minute? Sample answer: For each minute the shower runs, 6 gallons of water come out. So, if the shower ran 0 minutes, that would be 60 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 88 feet in second. d 88t 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 $7.0 for hours of work. W $7.0h 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

15 - NAME DATE PERID 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 6 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 6 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 6 feet tall who weighs 00 pounds, find a value for k in the equation s kh. 6. For a bab who is 0 inches long and weighs 6 pounds, find an infant value for k in the equation s kh. 7. According to the adult equation ou found (Eercise ), how much would an imaginar giant 0 feet tall weigh? 8. 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 7 and 8? Glencoe/McGraw-Hill 9 Glencoe Algebra

16 - NAME DATE PERID 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 8. 8 riginal equation 8 Subtract from each side. 8 (0, ) Divide each side b. Simplif. (, ) 8 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: 8, -intercept. slope:, -intercept. slope:, -intercept 7 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

17 - Model Real-World Data Eample NAME DATE PERID Stud Guide and Intervention (continued) Slope-Intercept Form MEDIA Since 997, the number of cable TV sstems has decreased b an average rate of sstems per ear. There were 0,9 sstems in 997. a. Write a linear equation to find the average number of cable sstems in an ear after 997. 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 997. 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 0,80 Simplif. There were about 0,80 cable TV sstems in 000. Number of Cable TV Sstems Cable TV Sstems N 0,900 0,800 0,700 0,600 0, Years Since 997 Source: The World Almanac Eercises ENTERTAINMENT In 99, 6.7% of all households with TV s in the U.S. subscribed to cable TV. Between 99 and 999, the percent increased b about 0.6% 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. 6. Find the population in 00. Percent of Households with TV Having Cable Percent Population (millions) P Years Since 99 Source: The World Almanac Projected United States Population P Years Since 00 Source: The World Almanac Glencoe/McGraw-Hill 9 Glencoe Algebra

18 - NAME DATE PERID Skills Practice Slope-Intercept Form Write an equation of the line with the given slope and -intercept.. slope:, -intercept:. slope:, -intercept: 7. slope: 6, -intercept:. slope: 7, -intercept:. slope:, -intercept: 6. slope:, -intercept: 9 7. slope:, -intercept: 8. slope: 0, -intercept: 8 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. 6. A Norfolk pine is 8 inches tall and grows at a rate of. feet per ear. 7. A Cairn terrier weighs 0 pounds and is on a special diet to lose pounds per month. 8. An airplane at an altitude of 000 feet descends at a rate of 00 feet per mile. Glencoe/McGraw-Hill 9 Glencoe Algebra

19 - NAME DATE PERID 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 $7 for a consultation plus $ per hour.. The population of Pine Bluff is 679 and is decreasing at the rate of 7 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 6 m Months Glencoe/McGraw-Hill 96 Glencoe Algebra Pages Written P

20 - 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 7 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 0.6 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 0.6 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 97 Glencoe Algebra

21 - NAME DATE PERID 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 98 Glencoe Algebra

22 - NAME DATE PERID 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). (8, ), m. (, ), m 6. (, ), m 7. (, ), m 0 8. (, ), m 9. (, ), m 6 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

23 - Write an Equation Given Two Points Eample NAME DATE PERID 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). (, 6), (7, 0). (0, ), (, 7) 6. (6, ), (, ) 7. (, ), (, ) 8. (0, ), (, ) 9. (, ), (7, 7) 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, 6) and ( 0, 0). Glencoe/McGraw-Hill 00 Glencoe Algebra

24 - NAME DATE PERID 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 6. (, ), m 7. (, 0), m 8. (, ), m 9. (, ), m Write an equation of the line that passes through each pair of points (, ) (, ) (, ) (, ) (0, ) (, ). (, ), (, ). (, ), (6, ). (, ), (, ) 6. (, ), (0, 6) 7. (, ), (, ) 8. (, 6), (, ) Write an equation of the line that has each pair of intercepts. 9. -intercept:, -intercept: intercept:, -intercept: Lesson -. -intercept:, -intercept:. -intercept:, -intercept:. -intercept:, -intercept: 8. -intercept:, -intercept: Glencoe/McGraw-Hill 0 Glencoe Algebra

25 - NAME DATE PERID 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 6. (, ), m Write an equation of the line that passes through each pair of points (, ) (, ) (0, ) (, ) (, ) (, ) 0. (0, ), (, ). (, ), (, 0). (, ), (, ). (0, ), (, ). (, 0), (, 6). (, 0), (, ) Write an equation of the line that has each pair of intercepts. 6. -intercept:, -intercept: 7. -intercept:, -intercept: intercept:, -intercept: 9. -intercept:, -intercept: 0. DANCE LESSNS The cost for 7 dance lessons is $8. 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 76 F at the 6000-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

26 - 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? Reading the Lesson Read the introduction to Lesson - at the top of page 80 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 997? Add 000 to the 996 population, which gives 79,000.. 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 6. 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

27 - 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 96 ml 0 C 8 ml C 7 ml 7 C 6 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 8. 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. 7 C. In 88, 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, 7, 6, 6 Glencoe/McGraw-Hill 0 Glencoe Algebra

28 - NAME DATE PERID 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 (6, ) and has a slope of. m( ) Point-slope form ( 6) m ; (, ) (6, ) Therefore, the equation is ( 6). 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. ( 7, ), m 6 6. (8, ), m 7. ( 6, 7), m 0 8. (, 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 (, 6).. Write the point-slope form of an equation for the horizontal line that passes through (, 0). Lesson - Glencoe/McGraw-Hill 0 Glencoe Algebra

29 - NAME DATE PERID 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 ( 6) in Write ( 8) standard form. in slope-intercept form. ( 6) riginal equation ( 8) riginal equation ( ) ( 6) Multipl each side b. Distributive Propert ( 6) Distributive Propert Add to each side. Distributive Propert 7 Subtract from each side. Therefore, the slope-intercept form of the 7 Add to each side. 7 Multipl each side b. equation is. Therefore, the standard form of the equation is 7. Eercises Write each equation in standard form.. ( ). ( 6). ( 9). ( ). ( ) 6. ( ) Write each equation in slope-intercept form. 7. ( ) 8. ( 6) 9. 8 ( 8) ( ). ( ) Glencoe/McGraw-Hill 06 Glencoe Algebra

30 - NAME DATE PERID 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. (, 6), m 8 6. (, ), m 7. (, 6), m 8. (, ), m 9. (, ), m Write each equation in standard form ( ). 7 ( ). ( ). 6 ( ). ( ) 6. 0 ( ) 7. ( ) 8. ( ) Write each equation in slope-intercept form. 9. ( ) 0. ( ). 6 ( ). ( ). 6( ). 8 ( ). ( 6) 6. ( 9) 7. Lesson - Glencoe/McGraw-Hill 07 Glencoe Algebra

31 - NAME DATE PERID 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. (, 6), m. (, ), m 0. (, ), m. ( 8, ), m 6. (, ), m Write each equation in standard form. 7. ( ) 8. 0 ( ) 9. 7 ( ) 0. ( ). ( ). 6 ( )..( )..( )..( ) Write each equation in slope-intercept form. 6. ( ) 7. 7( ) 8. ( ) 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 7, 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 $6 to rent the truck on a da when it is driven 8 miles.. Write the point-slope form of an equation to find the total charge for an number of miles for a one-da rental. 6. Write the equation in slope-intercept form. 7. What is the dail fee? Glencoe/McGraw-Hill 08 Glencoe Algebra

32 - 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 86 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 88 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

33 - NAME DATE PERID 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

34 -6 NAME DATE PERID 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 (, 6) and is parallel to the graph of. A line parallel to has the same slope,. Replace m with and (, ) with (, 6) in the point-slope form. m( ) Point-slope form 6 ( ( )) m ; (, ) (, 6) 6 ( ) Simplif. 6 Distributive Propert 8 Slope-intercept form Therefore, the equation is 8. Lesson -6 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.... (, ) ( 8, 7) 8 (, ). (, ),. (6, ), 6. (, ), 7. (, ), 0 8. (, 6), 9. (, 6), 0. Find an equation of the line that has a -intercept of that is parallel to the graph of the line 8.. Find an equation of the line that has a -intercept of that is parallel to the graph of the line 6.. Find an equation of the line that has a -intercept of that is parallel to the graph of the line 6. Glencoe/McGraw-Hill Glencoe Algebra

35 -6 NAME DATE PERID 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. 6 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.. (, ),. (, ),. (6, ), 7. ( 8, 7), 8. (6, ), 6 6. (, ), 7. ( 9, ), 8. (, ), 9. (6, 6), 6 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 8. Glencoe/McGraw-Hill Glencoe Algebra

36 -6 NAME DATE PERID 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 -6. (, ),. (, ), 6. (, ), 7. (, ), 8. (, ), 9. (, ), 6 0. (, ), 7. (, ),. (, ), 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.. (, ),. (, ),. (, 6), 6 6. (, ), 7. (, ), 8. (0, 0), 9. (, ), 0. (, ), 7. (0, ), 7. (, ), 0. (, ), 6 9. (, ), 8 6 Glencoe/McGraw-Hill Glencoe Algebra

37 -6 NAME DATE PERID 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.. (, ),. (, ),. (, 6),. (, ),. (, ), 6. (, ), 7. (, ), 8. (, ), 9. ( 8, ), 0. (, ), 9 8. (, 6),. (, ), 7 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. ( 6, ),. (, ), 7 6. (0, ), 7. (, ), 6 8. (, 7), 6 9. (, ), (0, ), 8. (, ), 0. (, ), 7. ( 6, ), 6. (, ), 6 9. GEMETRY Quadrilateral ABCD has diagonals A C and B D. Determine whether A C is perpendicular to B D. Eplain. A D B 6. GEMETRY Triangle ABC has vertices A(0, ), B(, ), and C(, 6). Determine whether triangle ABC is a right triangle. Eplain. C Glencoe/McGraw-Hill Glencoe Algebra

38 -6 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 -6 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 -6 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

39 -6 NAME DATE PERID 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 7 m m Glencoe/McGraw-Hill 6 Glencoe Algebra

40 -7 NAME DATE PERID 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 -7 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) Years Since 990 Source: The Wall Street Journal Almanac Number of Mutual Funds Number of Funds (thousands) Years Since 99 Source: The Wall Street Journal Almanac Glencoe/McGraw-Hill 7 Glencoe Algebra

41 -7 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 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, 6) and (999,.7). Find the slope..7 6 m m.7 Find b in.7 b b 0 b Therefore, an equation of a line of fit is.7 0. Eercises Refer to the table for Eercises. Years Since 99 NAME DATE PERID Stud Guide and Intervention (continued) Scatter Plots and Lines of Fit Hourl Wage 0 $. $.8 $.8 $.78 $.. Draw a scatter plot.. Write the slope-intercept form of an equation for the. Draw a line of fit for the data. line of fit. U.S. Production Workers Hourl Wage Hourl Wage (dollars) Years Since 99 Source: The World Almanac Students per Computer Students per Computer in U.S. Public Schools Year Source: The World Almanac Glencoe/McGraw-Hill 8 Glencoe Algebra

42 -7 NAME DATE PERID 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 Books Borrowed Lesson -7.. Weight-Lifting Repetitions Weight (pounds) Number of Newspapers Evening Newspapers Year Source: Editor & Publisher BASEBALL For Eercises 7, 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. 6. Use the points (99, 9.60) and (998,.60) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot. Average Price ($) Baseball Ticket Prices Year 7. Predict the price of a ticket in 00. Source: Team Marketing Report, Chicago Glencoe/McGraw-Hill 9 Glencoe Algebra

43 -7 NAME DATE PERID 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 6, 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. 6. Predict the number of cases in 00. ZS For Eercises 7 0, use the table that shows the average and maimum longevit of various animals in captivit. 7. Draw a scatter plot and determine what relationship, if an, eists in the data. U.S. Mumps Cases Year Cases Source: Centers for Disease Control and Prevention U.S. Mumps Cases Cases Year Longevit (ears) Avg Ma Source: Walker s Mammals of the World 8. 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

44 -7 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 -7 at the top of page 98 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 -7 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

45 NAME DATE PERID -7 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 0.7 F Albuquerque, New Meico :07 N. F Anchorage, Alaska 6: N.9 F Birmingham, Alabama : N.7 F Charleston, South Carolina :7 N 7. F Chicago, Illinois :0 N.0 F Columbus, hio 9:9 N 6. F Duluth, Minnesota 6:7 N 7.0 F Fairbanks, Alaska 6:0 N 0. F Galveston, Teas 9: N.9 F Honolulu, Hawaii :9 N 7.9 F Las Vegas, Nevada 6: N. F Miami, Florida :7 N 67. F Richmond, Virginia 7: N.8 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 8: 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? 6. 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