Lesson: Point-Slope Form of Linear Equations

Introduction

In this lesson, we will explore the point-slope form of linear equations, a helpful way to write the equation of a line when you have a point on the line and the slope.

Point-Slope Form

The point-slope form of a linear equation is given by: $y - y_{1} = m(x - x_{1})$ where:

• $(x_{1}, y_{1})$ is a point on the line
• $m$ is the slope of the line

Example

Let's find the equation of a line that passes through the point $(2, 3)$ with a slope of $4$.

1. Identify the point: $(x_{1}, y_{1}) = (2, 3)$
2. Identify the slope: $m = 4$
3. Substitute into the point-slope form: $y - 3 = 4(x - 2)$
4. This is the point-slope equation of the line.

Converting to Slope-Intercept Form

To convert to slope-intercept form ($y = mx + b$), we can simplify: $\\ y - 3 = 4x - 8 \\$ $y = 4x - 5$

Key Questions

• What does each variable represent in the point-slope form?
• How can you identify the slope from a given linear equation?
• How do you convert from point-slope form to slope-intercept form?

Summary

The point-slope form is a useful way to write the equation of a line when you have a specific point and the slope. Understanding how to manipulate this form will help you work with linear equations effectively.