Answer: The required rate of change is -8.
Step-by-step explanation: Given that the graph shows the side view of a water slide with dimensions in feet.
We are to find the rate of change between the points (0, ?) and (?, 40).
From the graph, we note that
the y co-ordinate for the x co-ordinate 0 is 80 and the x co-ordinate for the y co-ordinate 40 is 5.
So, the given two points are (0, 80) and (5, 40).
The rate of change for a function f(x) between the points (a, b) and (c, d) is given by
![R_c=\dfrac{d-b}{c-a}.](https://tex.z-dn.net/?f=R_c%3D%5Cdfrac%7Bd-b%7D%7Bc-a%7D.)
Therefore, the rate of change for the given function between the points (0, 80) and (5, 40) is
![R_c=\dfrac{40-80}{5-0}=\dfrac{-40}{5}=-8.](https://tex.z-dn.net/?f=R_c%3D%5Cdfrac%7B40-80%7D%7B5-0%7D%3D%5Cdfrac%7B-40%7D%7B5%7D%3D-8.)
Thus, the required rate of change is -8.