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Mathematics LibreTexts

2.9E: Exercises

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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=8x6

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=3x1

Exercise 2.9E.9

slope 35 and y-intercept (0,1)

Exercise 2.9E.10

slope 15 and y-intercept (0,5)

Answer

y=15x5

Exercise 2.9E.11

slope 34 and y-intercept (0,2)

Exercise 2.9E.12

slope 23 and y-intercept (0,3)

Answer

y=23x3

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

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (1, negative 2) is plotted. A line intercepts the y-axis at (0, negative 5), passes through the point (1, negative 2), and intercepts the x-axis at (5 thirds, 0).

Exercise 2.9E.18

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, 0) is plotted. A line intercepts the y-axis at (0, 4) and intercepts the x-axis at (2, 0).

Answer

y=2x+4

Exercise 2.9E.19

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (6, 0) is plotted. A line intercepts the y-axis at (0, negative 3) and intercepts the x-axis at (6, 0).

Exercise 2.9E.20

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (4, 5) is plotted. A line intercepts the x-axis at (negative 8 thirds, 0), intercepts the y-axis at (0, 2), and passes through the point (4, 5).

Answer

y=34x+2

Exercise 2.9E.21

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 2), intercepts the x-axis at (9 fourths, 0), and passes through the point (3, negative 1).

Exercise 2.9E.22

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 4) is plotted. A line intercepts the x-axis at (negative 2 thirds, 0), intercepts the y-axis at (0, negative 1), and passes through the point (2, negative 4).

Answer

y=32x1

Exercise 2.9E.23

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (2, negative 2) is plotted. A line running parallel to the x-axis intercepts the y-axis at (0, negative 2) and passes through the point (2, negative 2).

Exercise 2.9E.24

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 9 to 9. The point (negative 3, 6) is plotted. A line running parallel to the x-axis passes through (negative 3, 6) and intercepts the y-axis at (0, 6).

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=38x1

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=13x11

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=52x22

Exercise 2.9E.39

m=7, point (1,3)

Exercise 2.9E.40

m=4, point (2,3)

Answer

y=4x11

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=13x143

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=15x2

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=3x1

Exercise 2.9E.71

line y=2x3, point (1,3)

Exercise 2.9E.72

line y=3x1, point (2,3)

Answer

y=3x+3

Exercise 2.9E.73

line 3xy=4, point (3,1)

Exercise 2.9E.74

line 2xy=6, point (3,0)

Answer

y=2x6

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 x2=0, point (1,2)

Exercise 2.9E.80

line x6=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=34x2, point (3,4)

Exercise 2.9E.88

line y=23x4, point (2,4)

Answer

y=32x1

Exercise 2.9E.89

line 2x3y=8, point (4,1)

Exercise 2.9E.90

line 4x3y=5, point (3,2)

Answer

y=34x14

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 y3=0, point (2,4)

Exercise 2.9E.94

line y6=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 y1=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=13x143

Exercise 2.9E.113

Perpendicular to the line x2y=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.

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “find the equation of the line given the slope and y-intercept,”, “find an equation of the line given the slope and a point,” “find an equation of the line given two points,” “find an equation of a line parallel to a given line,” and “find an equation of a line perpendicular to a given line.” The rest of the cells are blank.

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?


2.9E: Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

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