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slope 3 and y -intercept ( 0 , 5 )

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slope 4 and y -intercept ( 0 , 1 )

y = 4 x + 1

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slope 6 and y -intercept ( 0 , −4 )

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slope 8 and y -intercept ( 0 , −6 )

y = 8 x 6

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slope −1 and y -intercept ( 0 , 3 )

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slope −1 and y -intercept ( 0 , 7 )

y = x + 7

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slope −2 and y -intercept ( 0 , −3 )

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slope −3 and y -intercept ( 0 , −1 )

y = −3 x 1

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slope 3 5 and y -intercept ( 0 , −1 )

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slope 1 5 and y -intercept ( 0 , −5 )

y = 1 5 x 5

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slope 3 4 and y -intercept ( 0 , −2 )

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slope 2 3 and y -intercept ( 0 , −3 )

y = 2 3 x 3

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slope 0 and y -intercept ( 0 , −1 )

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slope 0 and y -intercept ( 0 , 2 )

y = 2

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slope −3 and y -intercept ( 0 , 0 )

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slope −4 and y -intercept ( 0 , 0 )

y = −4 x

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In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

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.

m = 5 8 , point ( 8 , 3 )

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m = 3 8 , point ( 8 , 2 )

y = 3 8 x 1

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m = 1 6 , point ( 6 , 1 )

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m = 5 6 , point ( 6 , 7 )

y = 5 6 x + 2

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m = 3 4 , point ( 8 , −5 )

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m = 3 5 , point ( 10 , −5 )

y = 3 5 x + 1

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m = 1 4 , point ( −12 , −6 )

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m = 1 3 , point ( −9 , −8 )

y = 1 3 x 11

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Horizontal line containing ( −2 , 5 )

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Horizontal line containing ( −1 , 4 )

y = 4

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Horizontal line containing ( −2 , −3 )

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Horizontal line containing ( −1 , −7 )

y = −7

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m = 3 2 , point ( −4 , −3 )

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m = 5 2 , point ( −8 , −2 )

y = 5 2 x 22

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m = −7 , point ( −1 , −3 )

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m = −4 , point ( −2 , −3 )

y = −4 x 11

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Horizontal line containing ( 2 , −3 )

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Horizontal line containing ( 4 , −8 )

y = −8

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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.

( 3 , 1 ) and ( 2 , 5 )

y = −4 x + 13

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( 2 , 7 ) and ( 3 , 8 )

y = x + 5

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( −3 , −4 ) and ( 5 2 )

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( −5 , −3 ) and ( 4 , −6 )

y = 1 3 x 14 3

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( −1 , 3 ) and ( −6 , −7 )

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( −2 , 8 ) and ( −4 , −6 )

y = 7 x + 22

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( 6 , −4 ) and ( −2 , 5 )

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( 3 , −2 ) and ( −4 , 4 )

y = 6 7 x + 4 7

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( 0 , 4 ) and ( 2 , −3 )

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( 0 , −2 ) and ( −5 , −3 )

y = 1 5 x 2

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( 7 , 2 ) and ( 7 , −2 )

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( 4 , 2 ) and ( 4 , −3 )

x = 4

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( −7 , −1 ) and ( −7 , −4 )

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( −2 , 1 ) and ( −2 , −4 )

x = −2

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( 6 , 2 ) and ( −3 , 2 )

y = 2

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( 3 , −4 ) and ( 5 , −4 )

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( −6 , −3 ) and ( −1 , −3 )

y = −3

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( 0 , 0 ) and ( 1 , 4 )

y = 4 x

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( −2 , −3 ) and ( −5 , −6 )

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( −3 , 0 ) and ( −7 , −2 )

y = 1 2 x + 3 2

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( 8 , −1 ) and ( 8 , −5 )

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( 3 , 5 ) and ( −7 , 5 )

y = 5

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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.

line y = 4 x + 2 , point ( 1 , 2 )

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line y = 3 x + 4 , point ( 2 , 5 )

y = 3 x 1

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line y = −2 x 3 , point ( −1 , 3 )

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line y = −3 x 1 , point ( 2 , −3 )

y = −3 x + 3

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line 3 x y = 4 , point ( 3 , 1 )

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line 2 x y = 6 , point ( 3 , 0 )

y = 2 x 6

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line 4 x + 3 y = 6 , point ( 0 , −3 )

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line 2 x + 3 y = 6 , point ( 0 , 5 )

y = 2 3 x + 5

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line x = −3 , point ( −2 , −1 )

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line x = −4 , point ( −3 , −5 )

x = −3

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line x 2 = 0 , point ( 1 , −2 )

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line x 6 = 0 , point ( 4 , −3 )

x = 4

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line y = 5 , point ( 2 , −2 )

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line y = 1 , point ( 3 , −4 )

y = −4

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line y + 2 = 0 , point ( 3 , −3 )

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line y + 7 = 0 , point ( 1 , −1 )

y = −1

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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.

line y = −2 x + 3 , point ( 2 , 2 )

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line y = x + 5 , point ( 3 , 3 )

y = x

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line y = 3 4 x 2 , point ( −3 , 4 )

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line y = 2 3 x 4 , point ( 2 , −4 )

y = 3 2 x 1

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line 2 x 3 y = 8 , point ( 4 , −1 )

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line 4 x 3 y = 5 , point ( −3 , 2 )

y = 3 4 x 1 4

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line 2 x + 5 y = 6 , point ( 0 , 0 )

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line 4 x + 5 y = −3 , point ( 0 , 0 )

y = 5 4 x

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line y 3 = 0 , point ( −2 , −4 )

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line y 6 = 0 , point ( −5 , −3 )

x = −5

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line y -axis, point ( 3 , 4 )

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line y -axis, point ( 2 , 1 )

y = 1

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Mixed practice

In the following exercises, find the equation of each line. Write the equation in slope–intercept form.

Containing the points ( 4 , 3 ) and ( 8 , 1 )

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Containing the points ( 2 , 7 ) and ( 3 , 8 )

y = x + 5

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m = 1 6 , containing point ( 6 , 1 )

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m = 5 6 , containing point ( 6 , 7 )

y = 5 6 x + 2

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Parallel to the line 4 x + 3 y = 6 , containing point ( 0 , −3 )

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Parallel to the line 2 x + 3 y = 6 , containing point ( 0 , 5 )

y = 2 3 x + 5

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m = 3 4 , containing point ( 8 , −5 )

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m = 3 5 , containing point ( 10 , −5 )

y = 3 5 x + 1

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Perpendicular to the line y 1 = 0 , point ( −2 , 6 )

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Perpendicular to the line y -axis, point ( −6 , 2 )

y = 2

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Containing the points ( 4 , 3 ) and ( 8 , 1 )

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Containing the points ( −2 , 0 ) and ( −3 , −2 )

y = x + 2

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Parallel to the line x = −3 , containing point ( −2 , −1 )

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Parallel to the line x = −4 , containing point ( −3 , −5 )

x = −3

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Containing the points ( −3 , −4 ) and ( 2 , −5 )

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Containing the points ( −5 , −3 ) and ( 4 , −6 )

y = 1 3 x 14 3

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Perpendicular to the line x 2 y = 5 , containing point ( −2 , 2 )

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Perpendicular to the line 4 x + 3 y = 1 , containing point ( 0 , 0 )

y = 3 4 x

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Everyday math

Cholesterol. The age, x , and LDL cholesterol level, 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.

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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.

y = 1.2 x + 5.2

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Writing exercises

Why are all horizontal lines parallel?

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Explain in your own words why the slopes of two perpendicular lines must have opposite signs.

Answers will vary.

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Self check

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.

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?

Practice Key Terms 1

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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