Slope Formula

Slope

Formula

Summary

The slope of a line is calculated by the change in over the change in for any two points on the line. Another way of stating the slope of a line is the rise over the run.

Variable Description
The change in
The change in
The coordinates of the first point
The coordinates of the second point

Usage Notes

To calculate the slope of a line calculate the change in over the change in for two points along the line. Two points on a line form the shape of a right-triangle, which is a helpful visualization of the rise over run of a line.

Slope of Line Example 1
Slope of Line Example.

To calculate the slope of the line given by the equation we can substitute the coordinates of two points on the line into the formula below:

Steps
  1. Identitify two points to use to calculate the slope of the line. In this case, the point at and are natural choices. Any two points along the line will calculate the same slope.

    Equation of Line Example.
  2. Set up the slope formula shown below:

    Then substitute the coordinates of each point into the formula and compute the slope.

    The slope of the line given by the equation is equal to .