Graphs

The average rate of change measures how much a quantity changes per unit of change in its input. For two points \((x_1, y_1)\) and \((x_2, y_2)\), it is the change in output divided by the change in input: \(\frac{y_2-y_1}{x_2-x_1}\). For a function \(f\) on an interval \([a,b]\), compute \(\frac{f(b)-f(a)}{b-a}\). This is the slope of the secant line through the two points on the graph. The units are output units per input unit, such as miles per hour or dollars per year.