NAME

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DATE PERIOD

」esson l SkiI萱s P「actice

Consぬnt Rate of Change

Determine whether the relationship between the two quantities described in each table is Iinear. If so,範nd the

COnStant rate Of change. If not, eXPlain your reasonIng.

‾吋筑峨鴫∴ � �

l ��10

3 ��30

5 ��50

7 ��70

10 �100

15 �110

20 �200

25 �240

9 �60

10 �64

11 �68

12 �72

十二一　∵六へ �

¥十一p蝉誓言

5 �100

10 �120

15 �150

20 �130

Determine whether a proportional relationship e立sts betwee皿the two quanti慣es shown in each graph. Explain

yOur reaSOnIng.

36

y � � � � � � � �

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l

「 i � � � � �I

1 � � �i � �l X

2　　4　　6　　8　10

HourS After Storm

y � �圭 � � �〆 � � �

l � � � � � �

「‾ � � � � � �

l � � � � � �l

l �����1

さ � � �� ��X

1 2　3　4　5　6　7　8　9 10

NIlmber of Magazines

Course 3. Chapter 3 Equatjons in Two Va「iables

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2

　

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NAM巨

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DATE PERIOD

Lesson l Homewo「k Pract冒ce

Consfant Rate of Change

Deter皿ine whether the relationship between the two quantities described in each table is linear. If so,範nd the

COnStant rate Of change. If not, eXPlain your reasoning.

1. Fal)ric Needed for Costumes

2 �4 �6 �8

7 �14 �21 �28

For Exercises 3 and 4, refer to the graphs be量ow.

3.　Hawk Di血g丁oward P細ey

/へ

y � � � � � � � � � �

X ¥ �

之　　4　　6　　8　10

丁ime (S〉

a. Find the constant rate of change and interpret its

meanmg

b. Detemine whether a proportional血ear

relationship exists between the two quantities

Shown in the graph. Explain your reasoning.

Course 3. Chapter 3 Equations in Two Va「iables 35

2. Distance Traveled on Bike Trip

1 �2 �3 �4

21.8 �43.6 �68.8 �90.6

y � �露 �0 �Ok �S �ale �§ � � �

X

。■/

2　　4　　6　　8　10

Daγ

a. Find the constant rate of change and inteapret its

meanmg.

b. Detemine whether a proportional linear

relationship exists between the two quantities

Shown in the graph. Explain your reasonmg.

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NAM E DATE

Lesson 4 Sk雪看8s P「act雪ce/(¥

Slape-h tercep t Fbm

State the sIope and the y-intercept for the graph of each equation.

1.y=芳十4

4.y=「X十3

7.y葛2x=-1

10. Graph a line with a

SIope ofl and a

y-intercept of 」書.

y � � � � �i

1 i i � � �1 l � � �

○ � � � � �★ 」

2.y=2x-2

5・y=尋-5

8.y十上部=2

11. Graph a line with a

SIope of2 and a

y-intercept of -3.

1 �y � �! � � �

1 � �1 �l � � �

( �i � � � � �

ii �� �! i ���l 上

) �o � � � � �京

! � � � � � �

) � � � � � �

「 �� � l � �� � � �

Graph each equation using the sIope and the y-intercept・

13.yこ三㍍-3

16.y=」露-2

y � � � � �

i

l l � � � � � �

0 � � � � �★

14.y=-づ十1

y � �i � � �!

漢 � � � � �

o � �l l � � �★

I � � �� �」 �( � � �

y � � � � �

o � � � � �i★

F � � �� � � � � � i �� ���( † ��� � � �

PERIOD

3.yこ諒-1

6・y=-‡十4

9・y=-‡-3

12. Graph a line wi血a

sIope of尋d a

y-intercept of l.

y � � � � �

上 � � � � � � � � �i

i �o � � � � �★

15・y尋-2

y � � � � �

o � � � � �★

y � � � � �

! � � �i i � � �

i l � � �雪 上

○ � �l 1 � � �i文

Course 3. Chapter 3 Equations in Two Variables

NAM E DATE

」esson 4 Homewo「k Practice

SIqpe-血tenCep t fom

State the sIope and the y-intercept for the graph of each equation.

1.y=4x十1

4・y二言㌃3

2.y=-鉱:十5

5.y+3刀=-7

Graph each equation using the sIope and the y-intercept.

7.y=-2x十2

聞8.y十美=-3

y � � � �

0 � � � � �X

ハ, 10. CAMPING The entrance fee to the national pa血is

$15. A campsite fee is $15 per night. The total cost

y for a camping trip for x nights can be represented

by the equationy = 15芳+ 15.

a. Graph the equation.

b. Use血e graph to find the total cost for 4 nights・

C. Interpret the sIope and the y-intercept.

11. GEOMETRY Use the diagram shown.

隅田

X十y二90

a. Write the equation in sIope-intercept form.

b. Graph the equation.

′一、　　C. Use血e graph to find the value ofy ifx = 30.

Course 3. Chapter 3 Equations in Two Variabies 41

3.-ザ十y=4

6・y=幸十2

PERIOD

8 7 60 �y � � � � � � � �

50 40 � � � � � � � � �

30 20 10 � � � � � � � � �

∂ �1 �2　3　4　5　6　7　8★

80 � � � � � � � � �

60 � � � � � � � � �

40 � � � � � � � � �

20 � � � � � � � � �

e � �2 �0 �4 �0 �6 �0 �8 �0‾

NAME DATE PERIOD

」esson 3 Sk雪書寡s Practice

Equaffons m y = mX Fb仰

For Hxercises l-3, determine whether each linear珊nction is a direct variation. If so, State the constant of

Variation.

P血e高　書　、 �� �$5 �$10 �$15 �$20

$0.41 �$0.82 �$l.23 �$l.64

旦OurS声　一　二 ��11 �12 �13 �14

154 �167 �180 �193

Age声∴ �8 �9 �10 �11

G亘de,y、 �3 �4 �5 �6

For Exercises 4-121 y Varies directly with JC. Write an equation for the direct variation. Then範nd each value.

/〆ヽ 4・Ify二8when尤=3’findywhenx=45.

5. Ify=-4whenx= 10, findywhenx= 2.

6・ Ify=27 whenx= 8,血1dywhenx= 11.

7. Findywhenx= 12, ify= 2 whenJ= 5.

8. Findywhen#= 3, ify=1 whenx =葛9.

9. Findywhenx=-6, ify= 15 whenx=-5.

10. Ify = 20 whenx = 8, What is the value ofx wheny =J?

11. Ify =T30 whenx = 15’What is the value ofx wheny = 60?

12. Ify = 42 whenx = 15, What is the value ofx wheny = 70?

40 Course 3. Chapter 3 Equations in Two Va「iables

NAME

//‾ヽ

DATE

Lesson 3 Homewo「k P「act雪ce

Equaffons血y王mX Fom

l. ADVERTISING The number ofvehicles a

dealership se11s varies directly with the

money spent on advertising. How many

Vehicles does the dealership se11 for each

$1 ,000 spent on advertising?

PER!OD

DeaIership Sa書es

y � � � � � � � � � � �漢

r

之　　　4　　　6　　　8　　10　12

Adve競踊れg 6l,000,功

2. SNOWMOBILES Bruce rents snowmobiles to tourists. He charges $135 for 4 hours and $202.50 for 6 hours. What is

the hourly rate Bruce charges to rent a snowmobile?

3. SOLAR ENERGY The power abso血ed by a solar panel varies directly with its area. If an 8 square meter panel

absorbs 8,160 wa備S Ofpower, how much power does a 12 square meter solar panel absorb?

4. INSECT CONTROL Mr. Malone used 40 pounds ofinsecticide to cover l,760 square feet oflawn and 60 pounds to

cover an additiona1 2,640 square feet. How many pounds of insecticide would Mr. Malone need to cover his whole

/ヽ　lawnof4,480sq脚efeet?

Deter血ine whether each linear function is a direct variation. If so, State the constant ofvariation.

Vp賞u血e声ヘ音/し �2 �4 �6 �8

Mass,し辛、 �10 �20 �30 �40

富i血e声　音 ��8 �9 �10 �ll

Tem �p,y、: �68 �7重 �74 �77

5 �10 �15 �20 分喜営ons, �罵言∴

iles,y∴、 ��95 �190 �285 �380

Age詳 �3 �6 �9 �12

Height)、y, �28 �40 �52 �64

ALGEBRA Ify Varies directly with巧write an equa慣on for the direct variation. Then範nd eac血value.

9. Ify=-5 whenx=2, findywhenx = 8.

10. Findywhenx= 1, ify= 3 whenx =2.

11. Ify =-7 whenx = -21, What is the value ofx wheny = 9?

12. Find:持Wheny= 18, ify= 5 whenx=4.

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Course 3. Chapter 3 Equations in Two Va「iables 39

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NAME

・/、ヽ

一¥、

へ、

DATE

Lesson 2 Sk冒萱一s Pract冒ce

SIope

Find the sIope ofthe line that passes through each pair ofpoints.

1. A(」2,一1), B(2, 4)　　　　　　　2. C(0, 2), D⊂2, 0)

4. G⊂3,喜1), Hし2,一2)　　　　　　5. j(0, 6), Jし1, 1)

7. 0(1, -3), P(2, 5)

10. U(1,3),玖1, 5)

8. Q(1, 0), R(3, 0)

11. W(2, -2),Xしl, 1)

13. A(2,一1), B(-4, 4)　　　　　14. C(-2, 2), D(-4, 2)

16. q7, 4), H(2, 0)

19. 0(5, ÷3), P(-3, 4)

22.玖2, 2),歓葛5, -4)

38

17.均2,葛2), L(2, -3)

20. Qし1, -3), R(1, 2)

23. C(0, -2), D(3, 」2)

PERIOD

3. E(3, 4), F(4, 「2)

6.糾0,一2), L(2, 4)

9.邸0ク4),買1, 0)

12. 】千〇5, 0),劉÷2, 〇七)

15. E(-1,一事), F(「3, 0)

18. Mしl, -1), N(-イブ-5)

21. W(3, 25),X(l, 1)

24. G(-3, 5), Hし3, 2)

Course 3. Chapter 3 Equations in Two Variables

NAME

/へ¥

/‾¥、

DATE PERIOD

Lesson 2 Homework Practice

SIqpe

Find the sIope ofeach line.1醒　2醒　3醒

The points given in each table lie on a Iine. Find the sIope ofthe line. Then graph the l血e.

● �y � � � � � � �営

漢音 方 � � � � � � � �漢音

喜看 X

0 � � � � � �1 � �‾1

臆菓 漢音

● � � � � � � � �漢音 ● � � � � � � � �■

7. HOMES Find the sIope ofthe roofof a home that

rises 8 feet for every horizontal change of24 feet.

∠≦]8代

8. MOUNTAINS Find the sIope of a mountain that

descends lOO meters for every horizontal distance

Of l,000皿ete重s

「OO m [二二、ゝ

1、000 m

Fi皿d the sIope ofthe Iine that passes through each pair of points.

9.A(1, 3), B(4, 7)　　　　　　　10. q3, 5), D(2, 6)

12. SNOWFALL Use the graph at the ri卸v. It shows the depth

in feet of snow after each two-hour period during a

SnOWStorm.

a. Find血e sIope ofthe line.

b. Does the graph show a constant rate of change? Explain.

C. Ifthe graph is extended to the right, COuld you expect

the sIope to remain constant? Explain・

Cou「se 3. Chapter 3 Equations in Two Variables

1l. E(4, 0), F(5, 5)

醇0　2　4　6　8　喜0置2

Hour5

37

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