Slope of a line

The slope of a line is its inclination with respect to the abscissa axis and is given by the ratio between the variation in y and the variation in x

The slope of a line in the Cartesian plane is the inclination of the line with respect to the abscissa axis. Usually indicated with the letter 𝑚, it is expressed by a number that describes both the steepness and the direction of the line. It corresponds to the ratio between the change in the 𝑦-coordinate and the change in the 𝑥-coordinate:

Δ𝑦 (read “delta y”) is the change in 𝑦, i.e., the difference between the 𝑦-coordinates of any two points on the line. Δ𝑥 (read “delta x”) is the change in 𝑥, i.e., the difference between the 𝑥-coordinates of those same two points. Therefore, if the coordinates of two points on the line are known, it is possible to derive the slope by calculating the ratio between Δ𝑦 and Δ𝑥.

Deriving the slope from the coordinates of two points

For example, consider the line that passes through points A and B in the following graph.