Exercises
MyMathlab®
3)
8
Watch the videos
Download the
In MyMathlab
MyDashBoard App
Verbal and Writing Skills, Exercises 1 and 2
1. You are given two points that lie on a line. Explain how you would find an equation of the line.
z.
Suppose y = - ~x + 5. What can you tell about the graph by looking at the equation?
Write an equation of the line with the given slope and the given y-intercept. Leave the answer in slope-intercept form.
3. Slope ~, y-intercept (0, -9)
4.
Slope - ~' y-intercept (0, 5)
Write an equation of the line with the given slope and the given y-intercept. Express the answer in standard form.
5. Slope i, y-intercept ( 0, t)
6. Slope ~' y-intercept ( 0,
!)
and is
Find the slope andy-intercept of each of the following lines. Then use these to write an equation of the line.
ough
er in
7.
8.
9.
10.
11.
u.
14.
15.
o help
13.
151
152
Chapter
3 Equations and Inequal ities in Two Variables and Functions
Write each equation in slope-intercept form. Then identify the ~lope and they-intercept for each line.
16. 2.x- y = 12
17.
18. 2x - 3y = -8
19. 5x - 4y
20.
1
3x + 2y =
X -
21. 2x
7
y = 5
= -20
41
3
+ 4 y = -3
For each equation find the slope and they-intercept. Use these to graph the equation.
1
2
4
23. y = -x - 3
+4
22. y = 3x
y .•.
1
c
'x
'
...L. l
.......
24. 5x - 4y = -20
25. 5x
.: ... !
+ 3y = 18
y
Find an equation of the line that passes through the given point and has the given slope. Express your answer in slopeintercept form.
26. (6, 5), m =
1
3
'
28. (8,0),m=-3
'
'
29. (-7, - 2),m = 5
5
30. (0 -1) m = - -
'
1
2
27. (4 4) m = - -
3
31. (6, 0), m =
-51
Find an equation of the line passing through the pair of points. Write the equation in slope-intercept form.
32. (5, - 3) and (1, -4)
33. (-4, -1) and (3, 4)
35.
36. (4, 8) and ( -3, 8)
(~. -3) and(~. -5)
37.. (12, -3) and (7, -3)
4
Section 3.3 Graphs and the Equations of a Line
153
Find an equation of the line satisfying the conditions given. Express your answer in standard form.
38. Parallel to x - y = 4 and passing through (-3, 2)
39. Parallel to 5x - y = 4 and passing through ( -2, 0)
40. Parallel to 2y + x = 7 and passing through ( -5, -4)
41. Parallel to x = 3y - 8 and passing through (5, -1)
42. Perpendicular toy = 3x and passing through ( -3, 2)
43. Perpendicular to 2y = -3x and passing through
(6, - 1)
44. Perpendicular to x - 4y = 2 and passing through
(3, -1)
45. Perpendicular to x + 7y = -12 and passing through
(-4, -1)
To Th ink About. Without graphing, determine whether the following pairs of lines are (a) parallel, (b) perpendicular,
or (c) neither parallel nor perpendicular.
46. 5x- 6y = 19
6x + 5y = -30
3
49. y = --x- 2
4
6x +By= -5
+ Sy = 40
5y + 3x = 17
47. -3x
48. y
-2x- 3y
1
14
14y + 6x = 3
50. y
2
= 3x + 6
3
7
= -12
5
1
6
3
6x + Sy = -12
= - x--
51. y
= -x--
Optional Graphing Calculator Problems If you have a graphing calculator, use it to graph each pair of
equations. D o the graphs appear to be parallel?
52. y
=
-2.39x
+ 2.04 and y = -2.39x - 0.87
53. y = l.43x - 2.17 and y = l.43x + 0.39
Applications
Cost of H omes The median sale price of single-family homes in the United States has been increasing steadily. The increase
can be approximated by a linear equation of the form y = mx + b. The U.S. Census B ureau reported that in 2000 the
~edian sale price of a single-family home in the United States was $174,900. In 2010, the median sale price of a single-family
orne was $223,900. We can record the data as follows:
Number of Years
Since 2000
Price of Home
in Thousands of Dollars
0
174.9
10
223.9
Source: www.census.gov