2.9E: Exercises
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- Feb 3, 2021
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Practice Makes Perfect
Find an Equation of the Line Given the Slope and y-Intercept
In the following exercises, find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.
Exercise 2.9E.1
slope 3 and y-intercept (0,5)
Exercise 2.9E.2
slope 4 and y-intercept (0,1)
- Answer
-
y=4x+1
Exercise 2.9E.3
slope 6 and y-intercept (0,−4)
Exercise 2.9E.4
slope 8 and y-intercept (0,−6)
- Answer
-
y=8x−6
Exercise 2.9E.5
slope −1 and y-intercept (0,3)
Exercise 2.9E.6
slope −1 and y-intercept (0,7)
- Answer
-
y=−x+7
Exercise 2.9E.7
slope −2 and y-intercept (0,−3)
Exercise 2.9E.8
slope −3 and y-intercept (0,−1)
- Answer
-
y=−3x−1
Exercise 2.9E.9
slope 35 and y-intercept (0,−1)
Exercise 2.9E.10
slope 15 and y-intercept (0,−5)
- Answer
-
y=15x−5
Exercise 2.9E.11
slope −34 and y-intercept (0,−2)
Exercise 2.9E.12
slope −23 and y-intercept (0,−3)
- Answer
-
y=−23x−3
Exercise 2.9E.13
slope 0 and y-intercept (0,−1)
Exercise 2.9E.14
slope 0 and y-intercept (0,2)
- Answer
-
y=2
Exercise 2.9E.15
slope −3 and y-intercept (0,0)
Exercise 2.9E.16
slope −4 and y-intercept (0,0)
- Answer
-
y=−4x
In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.
Exercise 2.9E.17
Exercise 2.9E.18
- Answer
-
y=−2x+4
Exercise 2.9E.19
Exercise 2.9E.20
- Answer
-
y=34x+2
Exercise 2.9E.21
Exercise 2.9E.22
- Answer
-
y=−32x−1
Exercise 2.9E.23
Exercise 2.9E.24
- Answer
-
y=6
Find an Equation of the Line Given the Slope and a Point
In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.
Exercise 2.9E.25
m=58, point (8,3)
Exercise 2.9E.26
m=38, point (8,2)
- Answer
-
y=38x−1
Exercise 2.9E.27
m=16, point (6,1)
Exercise 2.9E.28
m=56, point (6,7)
- Answer
-
y=56x+2
Exercise 2.9E.29
m=−34, point (8,−5)
Exercise 2.9E.30
m=−35, point (10,−5)
- Answer
-
y=−35x+1
Exercise 2.9E.31
m=−14, point (−12,−6)
Exercise 2.9E.32
m=−13, point (−9,−8)
- Answer
-
y=−13x−11
Exercise 2.9E.33
Horizontal line containing (−2,5)
Exercise 2.9E.34
Horizontal line containing (−1,4)
- Answer
-
y=4
Exercise 2.9E.35
Horizontal line containing (−2,−3)
Exercise 2.9E.36
Horizontal line containing (−1,−7)
- Answer
-
y=−7
Exercise 2.9E.37
m=−32, point (−4,−3)
Exercise 2.9E.38
m=−52, point (−8,−2)
- Answer
-
y=−52x−22
Exercise 2.9E.39
m=−7, point (−1,−3)
Exercise 2.9E.40
m=−4, point (−2,−3)
- Answer
-
y=−4x−11
Exercise 2.9E.41
Horizontal line containing (2,−3)
Exercise 2.9E.42
Horizontal line containing (4,−8)
- Answer
-
y=−8
Find an Equation of the Line Given Two Points
In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.
Exercise 2.9E.43
(2,6) and (5,3)
Exercise 2.9E.44
(3,1) and (2,5)
- Answer
-
y=−4x+13
Exercise 2.9E.45
(4,3) and (8,1)
Exercise 2.9E.46
(2,7) and (3,8)
- Answer
-
y=x+5
Exercise 2.9E.47
(−3,−4) and (5,−2)
Exercise 2.9E.48
(−5,−3) and (4,−6)
- Answer
-
y=−13x−143
Exercise 2.9E.49
(−1,3) and (−6,−7)
Exercise 2.9E.50
(−2,8) and (−4,−6)
- Answer
-
y=7x+22
Exercise 2.9E.51
(6,−4) and (−2,5)
Exercise 2.9E.52
(3,−2) and (−4,4)
- Answer
-
y=−67x+47
Exercise 2.9E.53
(0,4) and (2,−3)
Exercise 2.9E.54
(0,−2) and (−5,−3)
- Answer
-
y=15x−2
Exercise 2.9E.55
(7,2) and (7,−2)
Exercise 2.9E.56
(4,2) and (4,−3)
- Answer
-
x=4
Exercise 2.9E.57
(−7,−1) and (−7,−4)
Exercise 2.9E.58
(−2,1) and (−2,−4)
- Answer
-
x=−2
Exercise 2.9E.59
(6,1) and (0,1)
Exercise 2.9E.60
(6,2) and (−3,2)
- Answer
-
y=2
Exercise 2.9E.61
(3,−4) and (5,−4)
Exercise 2.9E.62
(−6,−3) and (−1,−3)
- Answer
-
y=−3
Exercise 2.9E.63
(4,3) and (8,0)
Exercise 2.9E.64
(0,0) and (1,4)
- Answer
-
y=4x
Exercise 2.9E.65
(−2,−3) and (−5,−6)
Exercise 2.9E.66
(−3,0) and (−7,−2)
- Answer
-
y=12x+32
Exercise 2.9E.67
(8,−1) and (8,−5)
Exercise 2.9E.68
(3,5) and (−7,5)
- Answer
-
y=5
Find an Equation of a Line Parallel to a Given Line
In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.
Exercise 2.9E.69
line y=4x+2, point (1,2)
Exercise 2.9E.70
line y=3x+4, point (2,5)
- Answer
-
y=3x−1
Exercise 2.9E.71
line y=−2x−3, point (−1,3)
Exercise 2.9E.72
line y=−3x−1, point (2,−3)
- Answer
-
y=−3x+3
Exercise 2.9E.73
line 3x−y=4, point (3,1)
Exercise 2.9E.74
line 2x−y=6, point (3,0)
- Answer
-
y=2x−6
Exercise 2.9E.75
line 4x+3y=6, point (0,−3)
Exercise 2.9E.76
line 2x+3y=6, point (0,5)
- Answer
-
y=−23x+5
Exercise 2.9E.77
line x=−3, point (−2,−1)
Exercise 2.9E.78
line x=−4, point (−3,−5)
- Answer
-
x=−3
Exercise 2.9E.79
line x−2=0, point (1,−2)
Exercise 2.9E.80
line x−6=0, point (4,−3)
- Answer
-
x=4
Exercise 2.9E.81
line y=5, point (2,−2)
Exercise 2.9E.82
line y=1, point (3,−4)
- Answer
-
y=−4
Exercise 2.9E.83
line y+2=0, point (3,−3)
Exercise 2.9E.84
line y+7=0, point (1,−1)
- Answer
-
y=−1
Find an Equation of a Line Perpendicular to a Given Line
In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
Exercise 2.9E.85
line y=−2x+3, point (2,2)
Exercise 2.9E.86
line y=−x+5, point (3,3)
- Answer
-
y=x
Exercise 2.9E.87
line y=34x−2, point (−3,4)
Exercise 2.9E.88
line y=23x−4, point (2,−4)
- Answer
-
y=−32x−1
Exercise 2.9E.89
line 2x−3y=8, point (4,−1)
Exercise 2.9E.90
line 4x−3y=5, point (−3,2)
- Answer
-
y=−34x−14
Exercise 2.9E.91
line 2x+5y=6, point (0,0)
Exercise 2.9E.92
line 4x+5y=−3, point (0,0)
- Answer
-
y=54x
Exercise 2.9E.93
line y−3=0, point (−2,−4)
Exercise 2.9E.94
line y−6=0, point (−5,−3)
- Answer
-
x=−5
Exercise 2.9E.95
line y-axis, point (3,4)
Exercise 2.9E.96
line y-axis, point (2,1)
- Answer
-
y=1
Mixed Practice
In the following exercises, find the equation of each line. Write the equation in slope–intercept form.
Exercise 2.9E.97
Containing the points (4,3) and (8,1)
Exercise 2.9E.98
Containing the points (2,7) and (3,8)
- Answer
-
y=x+5
Exercise 2.9E.99
m=16, containing point (6,1)
Exercise 2.9E.100
m=56, containing point (6,7)
- Answer
-
y=56x+2
Exercise 2.9E.101
Parallel to the line 4x+3y=6, containing point (0,−3)
Exercise 2.9E.102
Parallel to the line 2x+3y=6, containing point (0,5)
- Answer
-
y=−23x+5
Exercise 2.9E.103
m=−34, containing point (8,−5)
Exercise 2.9E.104
m=−35, containing point (10,−5)
- Answer
-
y=−35x+1
Exercise 2.9E.105
Perpendicular to the line y−1=0, point (−2,6)
Exercise 2.9E.106
Perpendicular to the line y-axis, point (−6,2)
- Answer
-
y=2
Exercise 2.9E.107
Containing the points (4,3) and (8,1)
Exercise 2.9E.108
Containing the points (−2,0) and (−3,−2)
- Answer
-
y=x+2
Exercise 2.9E.109
Parallel to the line x=−3, containing point (−2,−1)
Exercise 2.9E.110
Parallel to the line x=−4, containing point (−3,−5)
- Answer
-
x=−3
Exercise 2.9E.111
Containing the points (−3,−4) and (2,−5)
Exercise 2.9E.112
Containing the points (−5,−3) and (4,−6)
- Answer
-
y=−13x−143
Exercise 2.9E.113
Perpendicular to the line x−2y=5, containing point (−2,2)
Exercise 2.9E.114
Perpendicular to the line 4x+3y=1, containing point (0,0)
- Answer
-
y=34x
Everyday Math
Exercise 2.9E.115
Cholesterol. The age, x, and LDL cholesterol evel, y, of two men are given by the points (18,68) and (27,122). Find a linear equation that models the relationship between age and LDL cholesterol level.
Exercise 2.9E.116
Fuel consumption. The city mpg, x, and highway mpg, y, of two cars are given by the points (29,40) and (19,28). Find a
linear equation that models the relationship between city mpg and highway mpg.
- Answer
-
y=1.2x+5.2
Writing Exercises
Exercise 2.9E.117
Why are all horizontal lines parallel?
Exercise 2.9E.118
Explain in your own words why the slopes of two perpendicular lines must have opposite signs.
- Answer
-
Answers will vary.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?