# 4.5: Graphs Using Slope-Intercept Form

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

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

• Identify the slope and \begin{align*}y-\end{align*}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:

• \begin{align*}m < 0\end{align*} when a line slants downward and \begin{align*}m > 0\end{align*} when it slants upward.
• \begin{align*}m = 0\end{align*} when a line is horizontal.
• \begin{align*}b < 0\end{align*} when the \begin{align*}y-\end{align*}intercept is below the \begin{align*}x-\end{align*}axis and \begin{align*}b > 0\end{align*} when it’s above the \begin{align*}x-\end{align*}axis.
• \begin{align*}b = 0\end{align*} 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 \begin{align*}m\end{align*} and \begin{align*}b\end{align*} one at a time in an equation in slope-intercept form. Make observations such as:

• The larger the \begin{align*}m\end{align*}, the steeper the line.
• Negative slopes can also represent steep lines. The smaller the \begin{align*}m\end{align*} (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 \begin{align*}y-\end{align*}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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