, .
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
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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
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['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.
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~ 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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.,-\- \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
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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)
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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