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### Course: Algebra (all content) > Unit 3

Lesson 8: Point-slope form# Point-slope form review

Review point-slope form and how to use it to solve problems.

## What is point-slope form?

Point-slope is a specific form of linear equations in two variables:

When an equation is written in this form, ${m}$ gives the slope of the line and $({a},{b})$ is a point the line passes through.

This form is derived from the slope formula.

*Want to learn more about point-slope form? Check out this video.*

## Finding point-slope equation from features or graph

### Example 1: Equation from slope and point

Suppose we want to find the equation of the line that passes through $({1},{5})$ and whose slope is ${-2}$ . Well, we simply plug ${m=-2}$ , ${a=1}$ , and ${b=5}$ into point-slope form!

### Example 2: Equation from two points

Suppose we want to find the line that passes through the points $(1,4)$ and $(6,19)$ . First, we use the two points to find the slope:

Now we use one of the points, let's take $({1},{4})$ , and write the equation in point-slope:

*Want to try more problems like this? Check out this exercise.*

## Finding features and graph from point-slope equation

When we have a linear equation in point-slope form, we can quickly find the slope of the corresponding line and a point it passes through. This also allows us to graph it.

Consider the equation $y-{1}={2}(x-{3})$ . We can tell that the corresponding line passes through $({3},{1})$ and has a slope of ${2}$ . Now we can graph the line:

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