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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.

Feb 22, 2012

Aug 22, 2014

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