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

Lesson 10: Summary: Forms of two-variable linear equations# Forms of linear equations review

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

There are three main forms of linear equations.

Slope-intercept | Point-slope | Standard |
---|---|---|

where | where | where |

## Example

A line passes through the points $(-2,-4)$ and $(-5,5)$ . Find the equation of the line in all three forms listed above.

Two of the forms require slope, so let's find that first.

Now we can plug in ${m}$ and one of the points, say ${(-5,5)}$ , to get $y-{{y}_{1}}={m}(x-{{x}_{1}})$ :

**point-slope form**,Solving for $y$ , we get $y={m}x+{b}$ :

**slope-intercept form**,And adding $3x$ to both sides, we get

**standard form,**$Ax+By=C$ :*Want another example? Check out this video.*

*Want to practice the different forms yourself? Check out this exercise.*

*Want a more in-depth review of each form? Check out these review articles:*

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