Answer
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 $(b, g(b))$.
Work Step by Step
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 $(b, g(b))$.
