Description of slope as the rate of change of a vertical variable with respect to a horizontal variable. Slope is defined as change in y over change in X, often described as rise over run. For a line, slope remains constant regardless of the points chosen. In calculus, tools are developed to analyze the instantaneous rate of change of a curve, where the rate of change may be constantly changing. Average rate of change can be calculated between two points as the slope of the line connecting them, known as the secant line. However, the slope between different points on the line varies, indicating changing rates of change. This leads to exploring the concept of instantaneous rate of change for curves with varying rates.