Final answer:
The average rate of change of the height over the entire slide is determined using two points on the height versus position curve. Without a second point, we can't calculate the change, but if provided, it's calculated using the formula for average rate of change (m) which is m = (change in height)/(change in x).
Step-by-step explanation:
The question asks for the average rate of change of the height over the entire slide. To find the average rate of change, we need two points on the slide's height versus position curve. We have one point given (when x = 20 feet, the height is 2 feet), but we need another point to calculate the rate of change (m).
Assuming we know the height at the start of the slide (which could be when x = 0), we can use the formula for average rate of change (m) which is m = (change in height)/(change in x). Without the starting height or another point on the slide, we cannot provide a numerical answer. If the height at the start of the slide is known, simply substitute the starting and ending heights and positions into the formula and solve for m.