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4.5: Graphs Using Slope-Intercept Form

Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Identify the slope and y-intercept of equations and graphs.
  • Graph an equation in slope-intercept form.
  • Understand what happens when you change the slope or intercept of a line.
  • Identify parallel lines from their equations.

Vocabulary

Terms introduced in this lesson:

slope-intercept form
rise
run
parallel lines

Teaching Strategies and Tips

Use Examples 1 and 2 to make observations such as:

  • m < 0 when a line slants downward and m > 0 when it slants upward.
  • m = 0 when a line is horizontal.
  • b < 0 when the y-intercept is below the x-axis and b > 0 when it’s above the x-axis.
  • b = 0 when a line passes through the origin.

Use the slope-intercept method to graph lines as an alternative to plotting and joining two intercepts.

With a graphing utility, demonstrate the effects on a line when changing m and b one at a time in an equation in slope-intercept form. Make observations such as:

  • The larger the m, the steeper the line.
  • Negative slopes can also represent steep lines. The smaller the m (more negative), the steeper the line.
  • Slopes approximately equal to zero represent lines that are almost horizontal.
  • Changing the intercept shifts a line up/down.
  • Parallel lines have the same slope but different y-intercepts.

Error Troubleshooting

In Example 2, use the marked lattice points and/or intercepts in the slope calculation for each line. Using these points allows students to obtain exact answers. See also Review Questions, Problems 2 and 3.

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CK.MAT.ENG.TE.1.Algebra-I.4.5

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