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# 5.2: Linear Equations in Point-Slope Form

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

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

• Write an equation in point-slope form.
• Graph an equation in point-slope form.
• Write a linear function in point-slope form.
• Solve real-world problems using linear models in point-slope form.

## Vocabulary

Terms introduced in this lesson:

point-slope form

## Teaching Strategies and Tips

Students learn to write linear equations in point-slope form given:

• The slope and any one point on the line (possibly the $y-$intercept). See Examples 1, 2, and 8.
• Any two points on the line ($m$ is not given). See Examples 3 and 7.

An equation in point-slope form:

• Uses subscripts on $x$ and $y$ to designate the fixed, given point. $x$ and $y$ assume any other points on the line.
• Is not solved for $y$. Suggest that students generate other values of $y$ by solving for $y$ first.
• Can be used to graph the line without having to rewrite the equation in slope-intercept form because a slope and a point determine a unique line. See Example 5.

Use Example 3 to show that any point on the line can be substituted for $(x_0,y_0)$. Point-slope equations will simplify to the same slope-intercept equation regardless of the chosen point.

Use Example 6 to introduce function notation for equations in point-slope form.

• Remind students that $f(5.5)=12.5$ is equivalent to the ordered pair $(5.5, 12.5)$ in $6b$.

“Flat fees”, initial amounts, starting times, etc. correspond to the intercept along the vertical axis.

## Error Troubleshooting

In Example 7, have students determine the independent and dependent variables first. This helps them form correct ordered pairs.

## Date Created:

Feb 22, 2012

Aug 22, 2014
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