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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 (x0, y0) and (x1, y1), the equation of the line joining them is:



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
Find x0, y0, x1 and y1.



Step 2
Insert the values of x0, y0, x1 and y1 into the equation.



Step 3
Tidy up the calculation.



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
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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: