How is the slope formula related to the definition of slope

The formula for slope measures the steepness (or angle) of a line by measuring the rise (y) over the run (x). Slope = Rise/Run.

Slope is the rise over the run or the rate at which something is changing which is the same as saying the slope is the change (or distance) in y over the change in x. the slope forumal is y2-y1/x2-x1. directly related to one anotehr