Slope Formula

Slope

Formula

Summary

The slope of a line is calculated by the change in over the change in . In other words, slope describes the rise over the run of the line.

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

Usage

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.

Example 1

Example Line

This example demonstrates how to calculate the slope of the line illustrated above using two points on the line.

Steps

  1. Identitify two points to use to calculate the slope of the line. The points at and are good choices. Any two points along the line will calculate the same slope.

    Example line with points labeled

  2. Set up the slope formula shown below:

    Then substitute the coordinates of each point into the formula and compute the slope. Note, the point with the smaller x-coordinate value should be used for the first point.

    Evaluate the arithmetic.

    The slope of the line is equal to .

Example 2

Example Line

This example demonstrates how to calculate the slope of the line illustrated above using two points on the line.

Steps

  1. Identitify two points along the line. The points at and are good choices. Any two points along the line will calculate the same slope.

    Example line with points labeled

  2. Set up the slope formula to calculate the rise over run of the line, visualized below ith the triangle. The bottom length of the triangle represents the change in and the height of the triangle represents the change in .

    Example line with points labeled

    The slope formula is shown below:

    Substitute the coordinates of each point into the formula and compute the slope. Note, the point with the smaller x-coordinate value should be used for the first point.

    Evaluate the arithmetic.

    The slope of the line is equal to .