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5.2: Linear Equations in Point-Slope Form

Difficulty Level: At Grade Created by: CK-12
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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.


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

An equation in point-slope form:

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

Notes/Highlights Having trouble? Report an issue.

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