Answer
The average rate of change of $y=g(t)$ over the interval [a,b] represents 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 given by: $\dfrac{Δy}{Δx}=\dfrac{[g(b)−g(a)]}{(b−a)}$.
Geometrically, the rate of change of $y=g(t)$ over the interval $[a,b]$ yields the slope of the line connecting the two points $[a,g(a)]$ and $[b,g(b)]$ and in a graph, a secant line represents a line connecting any two points.
Thus, we can interpret that the average rate of change of $y=g(t)$ over the interval [a,b] represents the slope of the secant line connecting the two points $[a,g(a)] \ and \ [b,g(b)]$.
