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Use slopes to determine if the lines 5 x + 4 y = 1 and 4 x + 5 y = 3 are perpendicular.

not perpendicular

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Use slopes to determine if the lines 2 x 9 y = 3 and 9 x 2 y = 1 are perpendicular.

not perpendicular

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Access this online resource for additional instruction and practice with graphs.

Key concepts

  • The slope–intercept form of an equation of a line with slope m and y -intercept, ( 0 , b ) is, y = m x + b .
  • Graph a Line Using its Slope and y -Intercept
    1. Find the slope-intercept form of the equation of the line.
    2. Identify the slope and y -intercept.
    3. Plot the y -intercept.
    4. Use the slope formula m = rise run to identify the rise and the run.
    5. Starting at the y -intercept, count out the rise and run to mark the second point.
    6. Connect the points with a line.



  • Strategy for Choosing the Most Convenient Method to Graph a Line: Consider the form of the equation.
    • If it only has one variable, it is a vertical or horizontal line.
      x = a is a vertical line passing through the x -axis at a .
      y = b is a horizontal line passing through the y -axis at b .
    • If y is isolated on one side of the equation, in the form y = m x + b , graph by using the slope and y -intercept.
      Identify the slope and y -intercept and then graph.
    • If the equation is of the form A x + B y = C , find the intercepts.
      Find the x - and y -intercepts, a third point, and then graph.
  • Parallel lines are lines in the same plane that do not intersect.
    • Parallel lines have the same slope and different y -intercepts.
    • If m 1 and m 2 are the slopes of two parallel lines then m 1 = m 2 .
    • Parallel vertical lines have different x -intercepts.
  • Perpendicular lines are lines in the same plane that form a right angle.
    • If m 1 and m 2 are the slopes of two perpendicular lines, then m 1 · m 2 = −1 and m 1 = −1 m 2 .
    • Vertical lines and horizontal lines are always perpendicular to each other.

Practice makes perfect

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 figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).

y = 4 x 2

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

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The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).

y = −3 x + 1

slope m = −3 and y -intercept ( 0 , 1 )

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The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).

y = 2 5 x + 3

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

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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 = −9 x + 7

−9 ; ( 0 , 7 )

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y = 4 x 10

4 ; ( 0 , −10 )

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4 x + y = 8

−4 ; ( 0 , 8 )

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8 x + 3 y = 12

8 3 ; ( 0 , 4 )

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7 x 3 y = 9

7 3 ; ( 0 , −3 )

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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.

Choose the Most Convenient Method to Graph a Line

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

y = −5 x + 2

slope–intercept

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y = 4 5 x 3

slope–intercept

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y = −1

horizontal line

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2 x 5 y = −10

intercepts

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y = 1 3 x + 5

slope–intercept

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Graph and Interpret Applications of Slope–Intercept

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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