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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\begin{align*}y-\end{align*}intercept). See Examples 1, 2, and 8.
• Any two points on the line (m\begin{align*}m\end{align*} is not given). See Examples 3 and 7.

An equation in point-slope form:

• Uses subscripts on x\begin{align*}x\end{align*} and y\begin{align*}y\end{align*} to designate the fixed, given point. x\begin{align*}x\end{align*} and y\begin{align*}y\end{align*} assume any other points on the line.
• Is not solved for y\begin{align*}y\end{align*}. Suggest that students generate other values of y\begin{align*} y\end{align*} by solving for y\begin{align*} y\end{align*} 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 (x0,y0)\begin{align*}(x_0,y_0)\end{align*}. 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\begin{align*}f(5.5)=12.5\end{align*} is equivalent to the ordered pair (5.5,12.5)\begin{align*}(5.5, 12.5)\end{align*} in 6b\begin{align*}6b\end{align*}.

“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.

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