Slope measures the steepness and direction of a line, calculated as the ratio of vertical change to horizontal change.
Slope = rise/run = Ξy/Ξx = (yβ - yβ)/(xβ - xβ). Positive slope = upward, negative = downward, zero = horizontal, undefined = vertical. Slope is constant for straight lines. In calculus, slope at a point on a curve is given by the derivative.
The concept of slope emerged from coordinate geometry developed by RenΓ© Descartes in the 17th century. The term "slope" came into common use in the 19th century.