Guide for finding the slope of a line

The equation used for finding slope (m) is:

m = Dy / Dx
(slope equals the change in y over the change in x)

where Dy = y2 - y1* and,
x1 ¹ x2

 1. First, find the coordinates of two points on the line. The coordinates of one point will be labeled (x1, y1), and the second will be (x2, y2). For example, we will pick the points (1.5, 2) and (9, 12).

2. Next, find the change in y and x.
For example:

Dy = y2 - y1 = 12 - 2 = 10 and,
Dx = x2 - x1 = 9 - 1.5 = 7.5

3. By definition, slope is the "rise over the run", or the y values over the x values. Divide the change of the y values by the change of the x values.

m = Dy / Dx = 7.5 / 10 = 0.75

Since this data is linear, you will get the same slope no matter which points you choose. The slope of the line is constant and equal to .75. This means that every increase of .75 units on the x axis will result in 1 unit of increase on the y axis.

*The change in y can be equal to y1 - y2 if and only if the change in x is equal to x1- x2. The order of subtraction doesn't matter as long as you are consistent with the order of both variables.

Copyright © 1997 Central Virginia Governor's School for Science and Technology Lynchburg, VA