Unit 9 Linear Functions (chapter 9)

Transcription

1 Unit 9 Linear Functions (chapter 9) Topics Functions Representing Linear Functions Constant Rate of Change and Slope Direct Variation Slope Intercept form Solve Sstems of equations b Graphing Solve Sstems of equations b Algebraicall Name: Team: Math Period: Teacher:

2 NAME DATE PERID Lesson Homework Practice Functions Determine whether each relation is a function. Eplain.. {(, -5), (0, -9), (, 0), (7, 0)}. {(5, ), (-, 5), (-7, 5), (, 5), (, 5), (-7, )} Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use If f () = + 5, find each function value. 7. f (). f (-0) 9. f () For Eercises, use the table, which shows the percent of emploed men and women in the U.S. labor force ever five ears from 95 to Is the relation (ear, percent of men) a function? Eplain. 0. f (-0) Emploed Members of Labor Force Year Men (% of male population) Women (% of female population) Describe how the percent of emploed men is related to the ear Is the relation (ear, percent of women) a function? Eplain.. Describe how the percent of emploed women is related to the ear

3 NAME DATE PERID Lesson Homework Practice Representing Linear Functions Find four solutions of each equation. Write the solutions as ordered pairs.. = - 5. = -7. = = 5. = = Graph each equation b plotting ordered pairs. 7. = -. + = 9. = = 7. = - 9. = Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation = 0.0 describes the approimate number of ounces in grams. a. Find three solutions of this equation. b. Draw the graph that contains these points. c. Do negative values of make sense in this case? Eplain. unces Grams Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

4 NAME DATE PERID Lesson Homework Practice Constant Rate of Change and Slope Find the constant rate of change for each linear function and interpret its meaning.. Fundraiser Profits. Profit ($) Cars Washed Time (seconds) Distance (ards) Find the slope of each line (, ) (0, ) (0, -) (0, -) (, -) (, -) Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use. Find the slope of the line that passes through each pair of points.. A(-0, ), B(-5, ) 7. C(7, -), D(, -). E(5, ), F(, -) 9. P(, ), Q(, -) 0. R(-, -), S(-, -5). T(-, ), U(, ). ne particularl large ant hill found in 997 measured 0 inches wide at the base and inches high. What was the slope of the ant hill?. Toda, the Great Pramid at Giza near Cairo, Egpt, stands 7 meters tall, coming to a point. Its base is a square with each side measuring 0 meters wide. What is the slope of the pramid?

5 NAME DATE PERID Lesson Homework Practice Direct Variation Determine if the relationship between the two quantities is a direct variation.. Number of Miles Number of Hours. Revenue ($) Glasses of Iced Tea Sold Determine whether the linear relationship is a direct variation. If so, state the constant of variation The cost of paper varies directl with the number of reams bought. Suppose reams cost $5.0. a. Write an equation that could be used to find the cost of reams of paper. b. Find the cost of 5 reams of paper.. Recall that the length a spring stretches varies directl with the amount of weight attached to it. A certain spring stretches 5 cm when a 0-gram weight is attached. a. Write a direct variation equation relating the weight and the amount of stretch. b. Estimate the stretch of the spring when it has a -gram weight attached. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

6 NAME DATE PERID Lesson 5 Homework Practice Slope-Intercept Form State the slope and the -intercept of the graph of each line.. - = = = Graph each equation using the slope and -intercept. -. = 5 5. = = -. = - 9. = A person weighing 50 pounds burns about 0 Calories per hour walking at a moderate pace. Suppose that the same person burns an average of 500 Calories per da through basic activities. The total Calories burned b that person can be represented b the equation = , where represents the number of hours spent walking. a. Graph the equation using the slope and b. State the slope and -intercept of the graph -intercept. of the equation and describe what the represent. 5 Calories Burned (thousands) Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use = Time Walking (h)

7 NAME DATE PERID Lesson Homework Practice Solve Sstems of Equations b Graphing Solve each sstem of equations b graphing.. = +. = -. + = = = + = -. = = 7. + = = - 5 = + = - 7. There are twice as man girls as bos in the school chorus. There are fewer bos than girls in the chorus. Write a sstem of equations to represent this situation. Then solve the sstem b graphing. Eplain what the solution means. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

8 NAME DATE PERID Lesson 7 Homework Practice Solve Sstems of Equations Algebraicall Solve each sstem of equations b substitution.. = -. = +. = - = = = -. = - 5. = -. = 0 + = = -5 = - 7. = 5 +. = - 9. = + 5 = - = 0 = 0. + =. = 9 -. = - = - = - - = -. = = 5. + = = = - - = -. The admission fee at a carnival is $5 for children and $ for adults. n Frida, 50 people attended the carnival and $700 was collected. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means. 7. Darci placed two orders for flowers and bushes. The first order was for flowers and bushes. The total of the first order was $. The second order was for flowers and bushes. The total of the second order was $90. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means.. The cost of muffins and quarts of milk is $. The cost of muffins and quart of milk is $7.50. Write a sstem of equations to represent this situation. Solve the sstem of equations b substitution. Eplain what the solution means. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

9 NAME DATE PERID Lesson Problem-Solving Practice Functions. Below are shirt sizes found in a department store, listed as (neck size, arm length). {(, ), (, 5), (, ), (5, ), (5, 5), (, ), (7, 5), (7, )} Does the relation (neck size, arm length) represent a function? Eplain.. The table below lists the average price of gasoline per gallon in the United States at the end of each month in a recent ear. Month Price Month Price Januar $. Jul $. Februar $. August $.75 March $.5 September $. April $.9 ctober $.5 Ma $.9 November $.07 June $.95 December $.0 Does the relation (month, price) represent a function? Eplain.. The information listed in the table shows the cost of a cab ride across town. Distance (miles) Price ($) Does the relationship between the distance traveled and the cost represent a function? Eplain. 5. The table below shows the tpical air temperature at various altitudes. Altitude (ft) Air Temperature ( F) ,000. 0, , , , , , , , , Eplain whether or not this relationship represents a function.. The table at the right shows the price of a book and its page content. Price ($) Pages Does the relation (price, pages) represent a function? Eplain.. Refer to the table in Eercise 5. Describe the relationship between altitude and air temperature. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

10 NAME DATE PERID Lesson Problem-Solving Practice Representing Linear Functions. n Januar, 00, the equation.99p = d represented the relationship between the U.S. dollar d and the British pound sterling p. Complete the following table. UK Pounds US Dollars. 0. The equation c =.5i can be used to convert between inches i and centimeters c. Complete the three ordered pairs (i, c) below. Round our answers to the nearest hundredth. (9., ), (,.), (.5, ).. Jerr bought material for a fence to put around the garden shown in the drawing. Garden House The equation + = 0 describes the relationship between the width and the length of his garden in feet. Find one ordered pair solution that makes sense in the situation and one that does not. Eplain our choices.. The cost of renting a car from the Frugal Car Rental Compan includes a $0 nonrefundable deposit and a travel cost of per mile. Find an equation to represent the total cost, C, if a car is rented and driven n miles. Then, find two ordered pairs that satisf this condition. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use. 5. Melissa is buing prizes for a school carnival. At the store, she finds colorful note paper sold in packs containing sheets and stickers sold individuall. She needs 50 prizes altogether. Melissa uses the equation p + s = 50 to help plan her purchase. Find three ordered pairs (p, s) that satisf this condition, and use them to graph the relationship.. Refer to the equation and graph in Eercise 5. Complete the following ordered pair: (, 0). Does this make sense for Melissa s purchase? Eplain.

11 NAME DATE PERID Lesson Problem-Solving Practice Constant Rate of Change and Slope. The graph shows the number of quarts of water the tpical person needs in a certain number of das. Find the constant rate of change for the relationship and interpret its meaning. Water Needed (qt) Lewis Count, Washington, has a guideline that new roads should not eceed a 5% grade, or a 5 foot rise over a horizontal distance of 00 feet. A proposed roadwa rises feet over 5 feet horizontall. Find the grade of the proposed roadwa to the nearest percent. Does it meet the count s guideline? Das. A part of trekkers left a staging hut, at an elevation of 5 feet, and arrived at their destination at an elevation of 7 feet. According to the map, the camps were 000 feet apart. What was the average slope between the two camps? 5. To function properl, a water outflow pipe must drop inch for ever inches of horizontal distance. Calculate the slope for this drain pipe.. Jennifer and a group of her friends are planning a hiking trip. Jennifer is in charge of making trail mi that will provide the group a total of 000 Calories. Raisins (oz) The graph shows the amount of peanuts and raisins she would have to bu in order to make the trail mi as planned. Find the constant rate of change for this linear function and interpret its meaning.. Refer to the information in Eercise 5. A design calls for a drainage pipe to cross a building 5 feet wide as it drops 5 inches. Is this pipe steep enough to function properl? Eplain Peanuts (oz) Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

12 NAME DATE PERID Lesson Problem-Solving Practice Direct Variation. The equation = 0 represents the number of hours Jennifer works in weeks. Determine if there is a constant of variation. If so, eplain what it means.. The amount of flour needed for a recipe varies directl with the number of servings planned. Three servings require cups of flour. Write a direct variation equation relating the number of servings s and the required number of cups of flour f. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.. Fresh Air Scuba Compan leases scuba diving equipment. The following table shows the cost of renting equipment for different lengths of time. Determine whether the relationship is a direct variation. Eplain. Das Cost ($) The table represents the number of feet Marco has left to climb down a mountain for hours Determine if the relationship between the two quantities is a direct variation. Eplain.. The distance a bus travels varies directl with time. A Red Lines bus has been traveling for.5 hours and has traveled a distance of.5 miles. The total distance it must cover on a particular route is 50 miles. How long will the bus take to cover this distance?. The equation = represents the number of dollars in McKenzie s saving account after months. Determine if there is a constant of variation. If so, eplain what it means.

13 NAME DATE PERID Lesson 5 Problem-Solving Practice Slope-Intercept Form. Rod is paid an overtime rate of $5 per hour after he earns his basic wage of $00 per week. Write an equation in slopeintercept form for the total pa p if he works h hours of over-time.. The monthl cost C of Marge s phone plan is given b C = 0 + m, where m is the number of etra minutes she uses in that month. Name the slope and -intercept in this situation, and eplain what each represents.. An elevator travels verticall in a building that has floors, each feet tall. The height h above the first floor after t seconds is given b h = 97 -.t. How long will it take for the elevator to reach the second floor?. Pete s bank account showed a balance at the beginning of the month of $0. He spent $.50 each da on bus tokens. The amount A left in his bank account after d das can be given b A = 0 -.5d. Graph the equation using the slope and -intercept. 5. Refer to the graph in Eercise. State the slope and -intercept of the graph, and describe what each represents.. Refer to the equation in Eercise. Find the -intercept and describe what it represents. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

14 NAME DATE PERID Lesson Problem-Solving Practice Solve Sstems of Equations b Graphing. Rachel and Kle both collect geodes. Rachel has less than twice the number of geodes that Kle has. Kle has fewer geodes than Rachel. Write a sstem of equations to represent this situation. Then solve the sstem of equations b graphing. Eplain what the solution means.. Michael has 9 five dollar bills and ten dollar bills in his wallet. The total amount in his wallet is $0. Write a sstem of equations to represent this situation. Then solve the sstem of equations b graphing. Eplain what the solution means. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.. Zan and Cleo both have sticker collections. Zan has 5 more than three times the number of stickers that Cleo has. Cleo has 5 fewer stickers than Zan Write a sstem of equations to represent this situation. Then solve the sstem of equations b graphing. Eplain what the solution means. 5. Tanner has more songs on his mp plaer than Amelia. Together the have songs. Write a sstem of equations to represent this situation. Then solve the sstem of equations b graphing. Eplain what the solution means How man solutions does the sstem of equations graphed at the right have? Eplain how ou know.. In one basketball game, Ran made 7 two point and three point baskets to score 7 points. Write a sstem of equations to represent this = + = - situation. Then solve the sstem of equations b graphing. Eplain what the solution means.

15 NAME DATE PERID Lesson 7 Problem-Solving Practice Solve Sstems of Equations Algebraicall. A concession stand sells hot dogs and hamburgers. At a football game, hot dogs and hamburgers were sold for $7. At another football game, 0 hot dogs and hamburgers were sold for $7. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means.. The sum of two numbers is. The difference between the numbers is. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means. Copright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.. Jose and Caroline went shopping for school supplies. Caroline spent $5.50 on 5 notebooks and folders. Jose bought notebooks and folders and spent $. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means. 5. Ms. Brockman wants to take her class on a trip to either the nature center or the zoo. The nature center charges $ per student, plus $95 for a -hour naturalist program. The zoo charges $9 per student plus $75 for a -hour guided tour. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution.. Gabe charges $0 to mow a lawn. Nate charges $5 to mow a lawn. Their total combined revenue one summer was $00. Nate mowed more lawns than Gabe. Write a sstem of equations to represent this situation. Then solve the sstem of equations b substitution. Eplain what the solution means.. Refer to the sstem of equations in Eercise 5. What does the solution mean?