Equation of a line given two points
This online calculator finds the equation of a line given two points on that line, in slopeintercept and parametric forms
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You can find an equation of a straight line given two points laying on that line. However, there exist different forms for a line equation. Here you can find two calculators for an equation of a line:

first calculator finds the line equation in slopeintercept form, that is,
It also outputs slope and intercept parameters and displays the line on a graph.  second calculator finds the line equation in parametric form, that is,
It also outputs a direction vector and displays line and direction vector on a graph.
Also, the text and formulas below the calculators describe how to find the equation of a line from two points manually.
How to find the equation of a line in slopeintercept form
Let's find slopeintercept form of a 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.
Finally, we use the calculated a and b to write the result as
Equation of a vertical line
Note that in the case of a vertical line, the slope and the intercept are undefined because the line runs parallel to the yaxis. The line equation, in this case, becomes
Equation of a horizontal line
Note that in the case of a horizontal line, the slope is zero and the intercept is equal to the ycoordinate of points because the line runs parallel to the xaxis. The line equation, in this case, becomes
How to find the slopeintercept equation of a line example
Problem: Find the equation of a line in the slopeintercept form given points (1, 1) and (2, 4)
Solution:
 Calculate the slope a:
 Calculate the intercept b using coordinates of either point. Here we use the coordinates (1, 1):
 Write the final line equation (we omit the slope, because it equals one):
And here is how you should enter this problem into the calculator above: slopeintercept line equation example
Parametric line equations
Let's find out parametric form of a 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
Equation of a vertical line
Note that in the case of a vertical line, the horizontal displacement is zero because the line runs parallel to the yaxis. The line equations, in this case, become
Equation of a horizontal line
Note that in the case of a horizontal line, the vertical displacement is zero because the line runs parallel to the xaxis. The line equations, in this case, become
How to find the parametric equation of a line example
Problem: Find the equation of a line in the parametric form given points (1, 1) and (2, 4)
Solution:
 Calculate the displacement vector:
 Write the final line equations:
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