# What Is the Equation of a Line that Passes through Two Points? (Mathematics Lesson)

# How to Find the Equation of a Line that Passes Through Two Points

A linear equation can be found that represents a line that passes two points.If the two points are

**(x**and

_{0}, y_{0})**(x**, the equation of the line joining them is:

_{1}, y_{1})# A Real Example of How to Find the Equation of a Line that Passes Through Two Points

**Question**: What is the equation of the line that passes through the points (1,2) and (4, 8)?

Step 1

**x**,

_{0}**y**,

_{0}**x**and

_{1}**y**.

_{1}Step 2

**x**,

_{0}**y**,

_{0}**x**and

_{1}**y**into the equation.

_{1}Step 3

The equation of the line that passes through the points (1,2) and (4,8) is

# Another Real Example of How to Find the Equation of a Line that Passes Through Two Points

The slider below gives another example of finding the equation of a line passing through two points:##### Interactive Test

**show**

##### Note

# THE FORMULA

The equation of a line passing through two points in made up of two equations.Start with the slope-point form of a linear equation:

Then replace the slope

**m**with the formula for the slope between two points:

# ALTERNATIVELY

It does not matter which of the two points is used to be subtracted from the**x**and the

**y**in the formula.

That is, the following forms of the equation are equally valid: