Vocabulary
constant of variation . . . . . . . . 326
parent function. . . . . . . . . . . . . 357
run . . . . . . . . . . . . . . . . . . . . . . . . 311
direct variation . . . . . . . . . . . . . 326
perpendicular lines . . . . . . . . . 351
slope . . . . . . . . . . . . . . . . . . . . . . 311
family of functions . . . . . . . . . 357
rate of change . . . . . . . . . . . . . . 310
transformation . . . . . . . . . . . . . 357
linear equation . . . . . . . . . . . . . 298
reflection . . . . . . . . . . . . . . . . . . 359
translation . . . . . . . . . . . . . . . . . 357
linear function . . . . . . . . . . . . . 296
rise . . . . . . . . . . . . . . . . . . . . . . . . 311
x-intercept . . . . . . . . . . . . . . . . . 303
parallel lines . . . . . . . . . . . . . . . 349
rotation . . . . . . . . . . . . . . . . . . . . 358
y-intercept . . . . . . . . . . . . . . . . . 303
Complete the sentences below with vocabulary words from the list above. Words
may be used more than once.
1. A(n)
?
is a “slide,” a(n)
?
is a “turn,” and a(n)
?
is a “flip.”
−−−−−−
−−−−−−
−−−−−−
2. The x-coordinate of the point that contains the
?
is always 0.
−−−−−−
?
, and the value of b is the
?
.
3. In the equation y = mx + b, the value of m is the
−−−−−
−−−−−
5-1 Identifying Linear Functions (pp. 296–302)
EXERCISES
EXAMPLES
Tell whether each function is linear. If so, graph
the function.
■ y = -3x + 2
Write the equation in
y = -3x + 2
standard form.
+ 3x + 3x
−−− −−−−−−
This is a linear function.
3x + y =
2
Tell whether the given ordered pairs satisfy a
linear function. Explain.
4.
Generate ordered pairs.
x
y = -3x + 2
(x, y)
-2
y = -3(-2) + 2 = 8
(-2, 8)
(0, 2)
(2, -4)
0
y = -3(0) + 2 = 2
2
y = -3(2) + 2 = -4
{
­ä]ÊÓ®
ä
{
{
■
Ý
Plot the points and connect
them with a straight line.
{
­Ó]Ê{®
y = 2x 3
This is not a linear function because x has an
exponent other than 1.
368
Untitled-5 368
7.
y
-3
5.
x
y
3
0
-3
-1
1
1
-1
1
1
2
1
3
3
3
3
{(-2, 5), (-1, 3), (0, 1), (1, -1), (2, -3)}
{(1, 7), (3, 6), (6, 5), (9, 4), (13, 3)}
Each equation below is linear. Write each equation
in standard form and give the values of A, B, and C.
Þ
­Ó]Ên®
6.
x
8. y = -5x + 1
10. 4y = 7x
x+2
9. _ = -3y
2
11. 9 = y
12. Helene is selling cupcakes for $0.50 each. The
function f (x) = 0.5x gives the total amount of
money Helene makes after selling x number
of cupcakes. Graph this function and give its
domain and range.
Chapter 5 Linear Functions
11/2/05 9:49:20 AM
5-2 Using Intercepts (pp. 303–308)
EXERCISES
EXAMPLE
■
Find the x- and y-intercepts of 2x + 5y = 10.
Let y = 0.
Let x = 0.
2x + 5(0) = 10
2(0)+ 5y = 10
2x + 0 = 10
0 + 5y = 10
2x = 10
5y = 10
5y
2x = _
10
10
_
_
= _
5
5
2
2
x=5
y= 2
The x-intercept is 5.
The y-intercept is 2.
Find the x- and y-intercepts.
13.
{
14.
Þ
Ó
{
Ý
{ Ó ä
Ó
Ó
Þ
{
Ó
Ý
ä
{
Ó
{
15. 3x - y = 9
16. -2x + y = 1
17. -x + 6y = 18
18. 3x - 4y = 1
5-3 Rate of Change and Slope (pp. 310–317)
EXERCISES
EXAMPLE
Find the slope.
19. Graph the data and
show the rates of
change.
i˜}̅ʭvÌ®
œ˜ÛiÀȜ˜ÊœvÊ
i>ÃÕÀi“i˜Ì
>ÃiÞ½ÃÊ
>ÃÃiÀœi
Time (s)
­Î]ʙ®
n
È
{
Ó
£
change in y
slope = __
change in x
3
_
= =3
1
­Ó]ÊÈ®
Î
­£]Êή
ä
£
Ó
Î
20. Find the slope of the
line graphed below.
{
i˜}̅ʭÞ`®
Distance (ft)
0
0
1
16
2
64
3
144
4
&ATG
■
3ERVINGS
256
5-4 The Slope Formula (pp. 320–325)
EXERCISES
EXAMPLE
■
Find the slope of the line described by
2x - 3y = 6.
Find the slope of the line described by each equation.
21. 4x + 3y = 24
22. y = -3x + 6
Step 1 Identify the x- and y-intercepts.
23. x + 2y = 10
24. 3x = y + 3
25. y + 2 = 7x
26. 16x = 4y + 1
Let y = 0.
2x - 3(0) = 6
2x = 6
x=3
Let x = 0.
2(0) - 3y = 6
-3y = 6
y = -2
The line contains (3, 0) and (0, -2).
Step 2 Use the slope formula.
y2 - y1 _
-2 - 0 _
-2 _
2
m=_
x 2 - x 1 = 0 - 3 = -3 = 3
Find the slope of the line that contains each pair
of points.
27. (1, 2) and (2, -3)
28. (4, -2) and (-5, 7)
( )
( )
29. (-3, -6) and (4, 1)
3, _
5
1 , 2 and _
30. _
4 2
2
31. (2, 2) and (2, 7)
32. (1, -3) and (5, -3)
Study Guide: Review
a107se_c05_0368-0377_4R.indd 369
369
5/13/06 12:57:26 PM
5-5 Direct Variation (pp. 326–331)
EXERCISES
EXAMPLE
■
Tell whether 6x = -4y is a direct variation. If
so, identify the constant of variation.
6x = -4y
-4y
6x
Solve the equation for y.
=
-4
-4
6x=y
-_
4
3x
Simplify.
y = -_
2
This equation is a direct variation because it
can be written in the form y = kx, where
k = - __32 .
_ _
Tell whether each equation is a direct variation. If so,
identify the constant of variation.
33. y = -6x
34. x - y = 0
35. y + 4x = 3
36. 2x = -4y
37. The value of y varies directly with x, and y = -8
when x = 2. Find y when x = 3.
38. Maleka charges $8 per hour for baby-sitting. The
amount of money she makes varies directly with
the number of hours she baby-sits. The equation
y = 8x tells how much she earns y for baby-sitting
x hours. Graph this direct variation.
5-6 Slope-Intercept Form (pp. 334–340)
EXERCISES
EXAMPLE
■
4
Graph the line with slope = - __
and
5
y-intercept = 8.
Step 1 Plot (0, 8).
Step 2 For a slope of
-4
___
, count
5
4 down and
5 right from (0, 8).
Plot another point.
n
{
{
{
Graph each line given the slope and y-intercept.
1 ; y-intercept = 4
39. slope = - _
2
Þ
­ä]Ên®
ä
40. slope = 3; y-intercept = -7
x
Ý
{
n
{
Step 3 Connect the two points with a line.
Write the equation in slope-intercept form that
describes each line.
1 , y-intercept = 5
41. slope = _
3
42. slope = 4, the point (1, -5) is on the line
5-7 Point-Slope Form (pp. 341–347)
EXERCISES
EXAMPLE
■
Write an equation in slope-intercept form for
the line through (4, -1) and (-2, 8).
y2 - y1 _
8 -(-1) _
3
9
_
m=_
x 2 - x 1 = -2 - 4 = -6 = - 2
y - y 1 = m(x - x 1)
y-8=-
_3 [x -(-2)]
2
3 (x + 2)
y - 8 = -_
2
3x-3
y - 8 = -_
2
3x+5
y = -_
2
370
Untitled-5 370
Find the
slope.
Substitute into the
point-slope form.
Solve for y.
Graph the line with the given slope that contains the
given point.
1 ; 4, -3
43. slope = _
44. slope = -1; (-3, 1)
)
(
2
Write an equation in point-slope form for the line
with the given slope through the given point.
45. slope = 2; (1, 3)
46. slope = -5; (-6, 4)
Write an equation in slope-intercept form for the line
through the two points.
47. (1, 4) and (3, 8)
48. (0, 3) and (-2, 5)
49. (-2, 4) and (-1, 6)
50. (-3, 2) and (5, 2)
Chapter 5 Linear Functions
11/2/05 9:49:25 AM