## University Calculus: Early Transcendentals (3rd Edition)

The average rate of change of the function $y=g(t)$ over the interval from $t=a$ to $t=b$ is $$\frac{\Delta y}{\Delta x}=\frac{g(b)-g(a)}{b-a}$$ The average rate of change of $y=g(t)$ over the interval $[a,b]$ is the slope of the secant line connecting two points $(a, g(a))$ and $(b, g(b))$.
The average rate of change of the function $y=g(t)$ over the interval from $t=a$ to $t=b$ is $$\frac{\Delta y}{\Delta x}=\frac{g(b)-g(a)}{b-a}$$ The rate of change of $y=g(t)$ over the interval $[a,b]$ is in fact geometrically the slope of the line connecting two points $(a, g(a))$ and $(b, g(b))$. At the same time, a secant line is a line that connects any two points in a graph. So we can say the average rate of change of $y=g(t)$ over the interval $[a,b]$ is the slope of the secant line connecting two points $(a, g(a))$ and $(b, g(b))$.