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# 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 This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8110/. Also, please do not modify any references to the original work (if any) contained in this content.

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. #### Second point

Line equation

Slope

Intercept

Digits after the decimal point: 2 #### Second point

Equation for x

Equation for y

Direction vector

Digits after the decimal point: 2

## 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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