# 5.2: Linear Equations in Point-Slope Form

## 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 intercept). See Examples 1, 2, and 8.
- Any two points on the line ( is not given). See Examples 3 and 7.

An equation in point-slope form:

- Uses subscripts on and to designate the fixed, given point. and assume any other points on the line.
- Is not solved for . Suggest that students generate other values of by solving for 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 . 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 is equivalent to the ordered pair in .

“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.