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x + y = −4

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y = x 1

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Graphing Linear Equations

Recognize the Relation Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

  1. Is the ordered pair a solution to the equation?
  2. Is the point on the line?

y = x + 4

( 0 , 4 ) ( −1 , 3 )

( 2 , 2 ) ( −2 , 6 )

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative x plus 4 is plotted as an arrow extending from the top left toward the bottom right.
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y = 2 3 x 1

( 0 , −1 ) (3, 1)

( −3 , −3 ) (6, 4)

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals two-thirds x minus 1 is plotted as an arrow extending from the bottom left toward the top right.

yes; yes  yes; no

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Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

Graph Vertical and Horizontal lines

In the following exercises, graph each equation.

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

Graphing with Intercepts

Identify the x - and y -Intercepts on a Graph

In the following exercises, find the x - and y -intercepts.

Find the x - and y -Intercepts from an Equation of a Line

In the following exercises, find the intercepts of each equation.

x y = −1

( −1 , 0 ) , ( 0 , 1 )

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2 x + 3 y = 12

( 6 , 0 ) , ( 0 , 4 )

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Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

Slope of a Line

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

Use m = rise run to find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

( −1 , −1 ) , ( 0 , 5 )

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( 3 , 5 ) , ( 4 , −1 )

−6

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( −5 , −2 ) , ( 3 , 2 )

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( 2 , 1 ) , ( 4 , 6 )

5 2

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Graph a Line Given a Point and the Slope

In the following exercises, graph each line with the given point and slope.

( −3 , 4 ) ; m = 1 3

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (negative 3, 4) and (0, 3) is plotted.

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x -intercept −4 ; m = 3

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y -intercept 1; m = 3 4

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (0, 1) and (4, negative 2) is plotted.

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Solve Slope Applications

In the following exercises, solve these slope applications.

The roof pictured below has a rise of 10 feet and a run of 15 feet. What is its slope?

The figure shows a person on a ladder using a hammer on the roof of a building.
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A mountain road rises 50 feet for a 500-foot run. What is its slope?

1 10

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Intercept Form of an Equation of a Line

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

In the following exercises, use the graph to find the slope and y -intercept of each line. Compare the values to the equation y = m x + b .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals two-thirds x plus 4 is plotted from the top left to the bottom right.

y = 2 3 x + 4

slope m = 2 3 and y -intercept ( 0 , 4 )

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Identify the Slope and y-Intercept from an Equation of a Line

In the following exercises, identify the slope and y -intercept of each line.

y = 5 3 x 6

5 3 ; ( 0 , −6 )

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4 x 5 y = 8

4 5 ; ( 0 , 8 5 )

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Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y -intercept.

In the following exercises, determine the most convenient method to graph each line.

Practice Key Terms 3

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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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