If $(x_0,y_0)$ and $(x_0 + \Delta x, y_0 + \Delta y)$ are two points on the curve, then the "average slope" of the curve between these two points is defined as the ration of change in $y$ to the change in $x$,
average slope= $\frac {\Delta y}{\Delta x}$
Why do we call it the average slope?
Best Answer
Note that $\Delta x$ and $\Delta y$ can be thought of as the change in $x$ and the change in $y$, respectively, between the two points: $P = (x_0, y_0)$ and $Q = (x_0+Δx,y_0+Δy)$.
So dividing $\frac {\Delta y}{\Delta x}$ gives us the average slope when summing the slopes of each point $R$ on the curve, which lies between $P$ and $Q$. It is the value of the change in $y$ over that interval, with respect to the change in $x$ over that same interval.