# Line equation from two points

This online calculator finds the equation of a line given two points it passes through, in slope-intercept and parametric forms

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These online calculators find the equation of a line from 2 points.

First calculator finds the line equation in slope-intercept form, that is, . It also outputs slope and intercept parameters and displays line on a graph.

Second calculator finds the line equation in parametric form, that is, . It also outputs direction vector and displays line and direction vector on a graph.

A bit of theory can be found below the calculators.

## Slope-intercept line equation

Let's find slope-intercept form of line equation from the two known points and .

We need to find slope *a* and intercept *b*.

For two known points we have two equations in respect to *a* and *b*

Let's subtract the first from the second

And from there

Note that *b* can be expressed like this

So, once we have *a*, it is easy to calculate *b* simply by plugging or to the expression above.

## Parametric line equations

Let's find out parametric form of line equation from the two known points and .

We need to find components of the **direction vector** also known as **displacement vector**.

This vector quantifies the distance and direction of an imaginary motion along a straight line from the first point to the second point.

Once we have direction vector from to , our parametric equations will be

Note that if , then and if , then

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