3.6E: Exercises
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- Jan 4, 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 3.6E.1
slope 3 and y-intercept (0,5)
Exercise 3.6E.2
slope 4 and y-intercept (0,1)
- Answer
-
y=4x+1
Exercise 3.6E.3
slope 6 and y-intercept (0,−4)
Exercise 3.6E.4
slope 8 and y-intercept (0,−6)
- Answer
-
y=8x−6
Exercise 3.6E.5
slope −1 and y-intercept (0,3)
Exercise 3.6E.6
slope −1 and y-intercept (0,7)
- Answer
-
y=−x+7
Exercise 3.6E.7
slope −2 and y-intercept (0,−3)
Exercise 3.6E.8
slope −3 and y-intercept (0,−1)
- Answer
-
y=−3x−1
Exercise 3.6E.9
slope 35 and y-intercept (0,−1)
Exercise 3.6E.10
slope 15 and y-intercept (0,−5)
- Answer
-
y=15x−5
Exercise 3.6E.11
slope −34 and y-intercept (0,−2)
Exercise 3.6E.12
slope −23 and y-intercept (0,−3)
- Answer
-
y=−23x−3
Exercise 3.6E.13
slope 0 and y-intercept (0,−1)
Exercise 3.6E.14
slope 0 and y-intercept (0,2)
- Answer
-
y=2
Exercise 3.6E.15
slope −3 and y-intercept (0,0)
Exercise 3.6E.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 3.6E.17
Exercise 3.6E.18
- Answer
-
y=−2x+4
Exercise 3.6E.19
Exercise 3.6E.20
- Answer
-
y=34x+2
Exercise 3.6E.21
Exercise 3.6E.22
- Answer
-
y=−32x−1
Exercise 3.6E.23
Exercise 3.6E.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 3.6E.25
m=58, point (8,3)
Exercise 3.6E.26
m=38, point (8,2)
- Answer
-
y=38x−1
Exercise 3.6E.27
m=16, point (6,1)
Exercise 3.6E.28
m=56, point (6,7)
- Answer
-
y=56x+2
Exercise 3.6E.29
m=−34, point (8,−5)
Exercise 3.6E.30
m=−35, point (10,−5)
- Answer
-
y=−35x+1
Exercise 3.6E.31
m=−14, point (−12,−6)
Exercise 3.6E.32
m=−13, point (−9,−8)
- Answer
-
y=−13x−11
Exercise 3.6E.33
Horizontal line containing (−2,5)
Exercise 3.6E.34
Horizontal line containing (−1,4)
- Answer
-
y=4
Exercise 3.6E.35
Horizontal line containing (−2,−3)
Exercise 3.6E.36
Horizontal line containing (−1,−7)
- Answer
-
y=−7
Exercise 3.6E.37
m=−32, point (−4,−3)
Exercise 3.6E.38
m=−52, point (−8,−2)
- Answer
-
y=−52x−22
Exercise 3.6E.39
m=−7, point (−1,−3)
Exercise 3.6E.40
m=−4, point (−2,−3)
- Answer
-
y=−4x−11
Exercise 3.6E.41
Horizontal line containing (2,−3)
Exercise 3.6E.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 3.6E.43
(2,6) and (5,3)
Exercise 3.6E.44
(3,1) and (2,5)
- Answer
-
y=−4x+13
Exercise 3.6E.45
(4,3) and (8,1)
Exercise 3.6E.46
(2,7) and (3,8)
- Answer
-
y=x+5
Exercise 3.6E.47
(−3,−4) and (5,−2)
Exercise 3.6E.48
(−5,−3) and (4,−6)
- Answer
-
y=−13x−143
Exercise 3.6E.49
(−1,3) and (−6,−7)
Exercise 3.6E.50
(−2,8) and (−4,−6)
- Answer
-
y=7x+22
Exercise 3.6E.51
(6,−4) and (−2,5)
Exercise 3.6E.52
(3,−2) and (−4,4)
- Answer
-
y=−67x+47
Exercise 3.6E.53
(0,4) and (2,−3)
Exercise 3.6E.54
(0,−2) and (−5,−3)
- Answer
-
y=15x−2
Exercise 3.6E.55
(7,2) and (7,−2)
Exercise 3.6E.56
(4,2) and (4,−3)
- Answer
-
x=4
Exercise 3.6E.57
(−7,−1) and (−7,−4)
Exercise 3.6E.58
(−2,1) and (−2,−4)
- Answer
-
x=−2
Exercise 3.6E.59
(6,1) and (0,1)
Exercise 3.6E.60
(6,2) and (−3,2)
- Answer
-
y=2
Exercise 3.6E.61
(3,−4) and (5,−4)
Exercise 3.6E.62
(−6,−3) and (−1,−3)
- Answer
-
y=−3
Exercise 3.6E.63
(4,3) and (8,0)
Exercise 3.6E.64
(0,0) and (1,4)
- Answer
-
y=4x
Exercise 3.6E.65
(−2,−3) and (−5,−6)
Exercise 3.6E.66
(−3,0) and (−7,−2)
- Answer
-
y=12x+32
Exercise 3.6E.67
(8,−1) and (8,−5)
Exercise 3.6E.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 3.6E.69
line y=4x+2, point (1,2)
Exercise 3.6E.70
line y=3x+4, point (2,5)
- Answer
-
y=3x−1
Exercise 3.6E.71
line y=−2x−3, point (−1,3)
Exercise 3.6E.72
line y=−3x−1, point (2,−3)
- Answer
-
y=−3x+3
Exercise 3.6E.73
line 3x−y=4, point (3,1)
Exercise 3.6E.74
line 2x−y=6, point (3,0)
- Answer
-
y=2x−6
Exercise 3.6E.75
line 4x+3y=6, point (0,−3)
Exercise 3.6E.76
line 2x+3y=6, point (0,5)
- Answer
-
y=−23x+5
Exercise 3.6E.77
line x=−3, point (−2,−1)
Exercise 3.6E.78
line x=−4, point (−3,−5)
- Answer
-
x=−3
Exercise 3.6E.79
line x−2=0, point (1,−2)
Exercise 3.6E.80
line x−6=0, point (4,−3)
- Answer
-
x=4
Exercise 3.6E.81
line y=5, point (2,−2)
Exercise 3.6E.82
line y=1, point (3,−4)
- Answer
-
y=−4
Exercise 3.6E.83
line y+2=0, point (3,−3)
Exercise 3.6E.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 3.6E.85
line y=−2x+3, point (2,2)
Exercise 3.6E.86
line y=−x+5, point (3,3)
- Answer
-
y=x
Exercise 3.6E.87
line y=34x−2, point (−3,4)
Exercise 3.6E.88
line y=23x−4, point (2,−4)
- Answer
-
y=−32x−1
Exercise 3.6E.89
line 2x−3y=8, point (4,−1)
Exercise 3.6E.90
line 4x−3y=5, point (−3,2)
- Answer
-
y=−34x−14
Exercise 3.6E.91
line 2x+5y=6, point (0,0)
Exercise 3.6E.92
line 4 x+5 y=-3, point (0,0)
- Answer
-
y=\frac{5}{4} x
Exercise \PageIndex{93}
line y-3=0, point (-2,-4)
Exercise \PageIndex{94}
line y-6=0, point (-5,-3)
- Answer
-
x=-5
Exercise \PageIndex{95}
line y-axis, point (3,4)
Exercise \PageIndex{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 \PageIndex{97}
Containing the points (4,3) and (8,1)
Exercise \PageIndex{98}
Containing the points (2,7) and (3,8)
- Answer
-
y=x+5
Exercise \PageIndex{99}
m=\frac{1}{6}, containing point (6,1)
Exercise \PageIndex{100}
m=\frac{5}{6}, containing point (6,7)
- Answer
-
y=\frac{5}{6} x+2
Exercise \PageIndex{101}
Parallel to the line 4 x+3 y=6, containing point (0,-3)
Exercise \PageIndex{102}
Parallel to the line 2 x+3 y=6, containing point (0,5)
- Answer
-
y=-\frac{2}{3} x+5
Exercise \PageIndex{103}
m=-\frac{3}{4}, containing point (8,-5)
Exercise \PageIndex{104}
m=-\frac{3}{5}, containing point (10,-5)
- Answer
-
y=-\frac{3}{5} x+1
Exercise \PageIndex{105}
Perpendicular to the line y-1=0, point (-2,6)
Exercise \PageIndex{106}
Perpendicular to the line y-axis, point (-6,2)
- Answer
-
y=2
Exercise \PageIndex{107}
Containing the points (4,3) and (8,1)
Exercise \PageIndex{108}
Containing the points (-2,0) and (-3,-2)
- Answer
-
y=x+2
Exercise \PageIndex{109}
Parallel to the line x=-3, containing point (-2,-1)
Exercise \PageIndex{110}
Parallel to the line x=-4, containing point (-3,-5)
- Answer
-
x=-3
Exercise \PageIndex{111}
Containing the points (-3,-4) and (2,-5)
Exercise \PageIndex{112}
Containing the points (-5,-3) and (4,-6)
- Answer
-
y=-\frac{1}{3} x-\frac{14}{3}
Exercise \PageIndex{113}
Perpendicular to the line x-2 y=5, containing point (-2,2)
Exercise \PageIndex{114}
Perpendicular to the line 4 x+3 y=1, containing point (0,0)
- Answer
-
y=\frac{3}{4} x
Everyday Math
Exercise \PageIndex{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 \PageIndex{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=1.2 x+5.2
Writing Exercises
Exercise \PageIndex{117}
Why are all horizontal lines parallel?
Exercise \PageIndex{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?