, .

Name: Class: Date: _ ID: A

1. Jennifer is a car saleswoman. She is paid a salary of $1600 per month plus $400 for each car that she sells.Her salary can be modeled by the equation I(x) = 400x + 1600 where x is the number of cars sold. Graph this

Gu.ationand give its domain and range. .,a. I(x) ./ c. 1M.. 5000 ,/ 5000 I

- ~ . ,,-- ",,- :/_ §: 4000 /

/./ ta"__ " ca I

" [/') 3000 "/- c-, I

- ~ I" C I

•" 0 I2000 .: ::is 2000 ~

III

1000 / (\ot LOYYt~ ~ \Y\-\{YCtp"

Linear Function Review

§ 4000

taca[/') 3000;>..

~co::is

246 8 xNumber of Cars Sold

1000

D: {O, 1,2,3, ...}R: {$1600, $2000, $2400, $2800, ...}

b.

2 4 6 8Number of Cars Sold

5000

§: 4000

~ca[/') 3000b-sco::is 2000

1000

\s X \JQ\\JeS

'~'i \J Cl\ueSpoVl\(} \ '(\

'<--CAYl~~

(~e:se (A<e \')O-T

LOX''(e-L-~)

2 4 6 8 xNumber of Cars Sold

D: {$400, $2000, $3600, $5200, ...}R: {O, 1,2,3, ...}

d.

2 468 xNumber of Cars Sold

1M I•III

IIII

5000

§: 4000

~ca[/') 3000;>..

~s::o::is 2000

IIIII,,•,

I,,1000 / '(\ O-t

x

D: {O, 1,2,3, ... }R: {$400, $2000, $3600, 5200, ...},

1

, .

Name: --------------------- ID: A

D 2. Tell whether the slope ofthe line is positive, negative, zero, or undefmed. . .

4

-\ \tit-V e. \ sDO y \-se

o =0Y\A.V1

y

e.YO lero -3

2

-5 .-4 -3 -2 -1 1 2 3 4 5 .<-1

-2

-3

-4

-5

a. negative c. positiveb. undefmed ® zero b

3. Write the equation that describes the line with slope =!1 andy-intercept =% in slope-intercept form.

a. y=%x-% Q y=-%x+ % ~=- VY\ X -t b3 5 3 5

b. X=-2"Y+2" d. -2"x+y=2"

4. Identify each graph as being a non-linear function, linear function, or not a function.

f\JY'6t\OY\ -ro.sses vevtl uv\iY\t, t(st

\i\'\ellY -)1Y t'.\ q'yr\- \"' V\e

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Graph A GraphB GraphC

1 2 3 4 x

y y5

24

-3 -2 -J-I

-2 fvnvi'oV\-3 Nof l'Yl( tl'y

J 2 3 x -2 -I-I

-2

-3-J x

-I

a. Graph A: not a functionGraph B: not a functionGraph C: linear function

b. Graph A: non-linear functionGraph B: not a functionGraph C: not a function

Graph A: non-linear functionGraph B: linear functionGraph C: not a function

d. Graph A: non-linear functionGraph B: linear functionGraph C: linear function

2

Name: --~----------------- ID: A

6. Find the slope of the line.~.

1I

s ndeA1Y1ec\y

10

6

4

2

~'4-~++~~~¥+~~~r+~-10 -8 --{) -4 -2

-2-4

--{)

8 10 .r -4o

~QV\ V10+cl\\J\c1L by

Z-~Y-D \.

1---7-8

-10

ca. -2G undefined

7. Find the x- and y-intercepts.

c. 4d. 0

-10 -8 --{) -4

a. x-intercept: 2, y-intercept: -6b. x-intercept: -2, y-intercept: 6

x-intercept: 2, y-intercept: 6x-intercept: 6, y-intercept: 2

4

Name: -------------------- ID: A

5. Jim drove for several hours, recording the distance he had traveled in miles. Graph the data and show therates of change.

IHours5~ I 4

I6

I7

I10

220 300 320 500Miles

0- "I" .1- l y 'i350

2300

Vl 100..,:;:: 250::E 3 (l.\ ,2 DO)200 440

150 Y\\Yt 3

100 LDY( tbt 2

50

I 2 3 4 5 6 x

GHours Xy

400 400

350 350

300 @'OO'"~ 250

..,::::: 250 3::E

200 70 200

150 150

100 100

50 50

I 2 3 4 5 6 7 .T

Hours

8. Find the slope of the line.y

~,,:: ..•,h r\ n./

['I »:l. (./

/I..).

,/

/

./x

y

170

y

3

X (Ay\d Y~5PO -10-l-0-15~O-201::::;0:::::25=0=1301;;;;0,,~.\J'n.\ Ve s> V\ 0 t

Hours CDYY~C{

4

220

I 2 3~ x

~

X ClV1d ~ (A""\s V\O+CbvY'eL-t

rise S'\ope'fUY\

~ 'L--"'/ l-S 2.., -3c. ~ 'f~X 5-22

G z3

3

Name: -----------------------D

ID: A

9. A clothing manufacturer needs 2.4 yards of fabric to make a jacket and 1.6 yards of fabric to make amatching skirt. The number of jackets, x, and coats, y, that can be made from a 48-yard bolt of fabric can bere~resented by the equatio~ 2.4x + 1.6y = 48) Graph the function and fmd its intercepts. What does they-mtercept represent?a. c.

30

y

\\

\.

\

'"t 24:;;:'"4-0

o 18t.nSZ 12

6

12 18 24

Number of jackets

The y-intercept is (0, 24). The y-interceptgives the total number of jackets that canbe made from one bolt of fabric whenonly jackets are made.

6 30 x

b.y

<,I'.<,

I'.<,1"-

"-1"-

<,r-,

1"-<,

r-,

"- I'.

45

36

'"t 27:;;:..,4-0

:: 18<I).nSZ 9

9 18 27 36 45

Number of jackets

The y-intercept is (0, 48). The y-interceptgives the total number of skirts that canbe made from one bolt of fabric whenonly skirts are made.

L.4~ + \ .lDy ~4~-1.L\-x -2 '\'~x

\.loi 2·4x+4~\.~ \.lo l.lo

6

~:=-\,SX+~O

-

30

y

<,

I'-...

I'-.<,

I'-...

"'-

..,r; 24:;;:<I)

'+-<

:: 18<I)x:SZ 12

6

6 12 18 24 30 x

Number of jackets

The y-intercept is (30, 0). The y-interceptgives the total number of jackets that canbe made from one bolt of fabric whenonly jackets are made.

30

y

\\.

\

\1\

\

~ 24:Q

<I)

'+-<

~ 18.,.nSZ 12

6

6 12 18 24 30 x

Number of jackets

The y-intercept is (0, 30). The y-interceptgives the total number of skirts that canbe made from one bolt of fabric whenonly skirts are made.

'5D\\Jt fDv Y.

~ Hf\<, ~ \Y\t of-1~~M~+b

Name: ------------------- ID: A

10. Tell whether the function y = 5x - 2 is linear. If so, graph the function.'t Not a linear function. c.

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+O'(YY\ I

.,-\- \S \ \V'\{~Y'

-5 -4 -3 -2

lL 11.

y

5

4

- =4 -3 -2

-2

-3

-4

-5

OJI-5 -4 -3

The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. Thecosts of a fill-up and a car wash for three different customers are shown in the table. Write an equation forthe function in slope-intercept form. Then, find the cost of a fill-up and a car wash for a customer with atruck whose tank size is 29 gallons.

Tank size (gal) Total cost ($)(x) /tx)7 18.4012 29.4018 42.60

a. I(x) 0.45xb. I(x) 2.00x

I(x) 2.30xI(x) = 2.20x

1.36; Cost for truck = $14.412.75; Cost for truck = $60.752.75; Cost for truck = $69.453.00; Cost for truck = $66.80

ell ,~ .1-\ 0)( \1- \ ~G1.40')

7

1\ :1]5

Name: ~-------------- ID: A

G 12. Graph the line with a slope of 3 that contains the point (3, 6).

a. . G

Write an equation in slope-intercept form of the line with slope 6 that contains the point (~,1). ?\ \J~ \ Y\ Xa. y = 6x + 5 3 ::(to· S)t- 5 c. y = 6x + 3 '3:: (0 (c;) + '3 lAVid '( Sceb. y=6x-30 3~C~,S)- 30 @ y=6x-27 3 -:. lo(s)-g.,l l.f 't )

14. Find the slope of the line described by ~ - 3y = 36. +1.\- '/. . \ YY\G\'Le Sa. ~ So\\)e foy y t4 Q -~ _3 -~tt)( 3(0 It 1Yve.,b

3 d 3 "'l. __(\ . "4 . -"4 - -':) -~ - ~

\....., 15. Write an equation i for the line that has a slope of \. and contains the point (-9,8).

a. y-9=f(x+8) G y+8=;(x-9) "vn X, 'IIb. x+9=;(y-8) d. y-8=f(x+9)

y //

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v:V ~.

7- 0 ~ ~ l- X

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c

y /0

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/y /

II

-III

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8

Name: _ ID: A

20

Guseintercepts to graph the line described by=-2x +4y = -16.

a. x-intercept: 8, y-intercept: -4 . x-intercept: 8, y-intercept: -3y y

10 10

8

6

4

2

-10 -8 -6 -4 -2-2

6

4

2

b ' 8 x ec\LD'(~

-6 (10\ \ f-\-8 "\

-10

8 x

-8

-10

6

d. tntercept: Z}-inte;cept: -4

10

8

x-intercept: 7,y-intercept: -3y

4

2

6

4

10

8

2

-10 -8 -6 -4 x

-6

-8

-10

~D\ve

- 2x t4" ::-llPt1-X -+Zx

4\1 ::::--\ to t2 X-4 ---rtlf~ - -4 + t i

10

Name: ID: A

fL ..2l. Write the equation 4x +8y = -16 in slope-intercept form. Then graph the line described by the equation.

)I

1 Ia. Y=-"2x-2

y at cp(l~c. Y=-"2x-2

y

10 10

(OVV~8 8

'.. . ('. ~(.6 V) ') \ '()~ -€t 6

\,\0-\<I '\ \'{\~-10 -8 ~ -4 2 4 6 8 x -10 -8 ~ -4 x

-4

-6

~ -8

-10 -10

G 1 d. I o-lf(i~"o,J.~y =-"2 x-2 Y=-"2x-2r: y

10 10 Y\O'\8 8 )\o'f6 6

<I 4'.

2 "2 ·1

-10 ~ -6 -4 - x -10 -8 -6 -4 -2 4 6 8 x

-4 -4

~ -6

~ -8

-10 -10

A 22. The graph shows a linear relationship. Find the slope.

2

x10

8

6

4

-10 -8 -6 -4 -2-2-4

-6

-8

-10

Q 3 5C. 13

b. 13 d..!..

5 3