Question

the average rate of change from x = 0 to x = 15 is about -14/3. what does this mean in terms of the waterslide, from x = 0 to x = 15? on average, the slide rises 3 feet for every 14 feet of horizontal distance. on average, the slide rises 14/3 feet for every 1 foot of horizontal distance. on average, the slide drops 3 feet for every 14 feet of horizontal distance. on average, the slide drops 14/3 feet for every 1 foot of horizontal distance.

Explanation:

Step1: Understand average rate of change

The average rate of change $\frac{\Delta y}{\Delta x}$ represents the change in the vertical - direction ($y$) per unit change in the horizontal - direction ($x$). Here, the average rate of change is $-\frac{14}{3}$. A negative rate of change means the function (height of the waterslide) is decreasing as the horizontal distance ($x$) increases.

Step2: Interpret the fraction

The fraction $-\frac{14}{3}$ can be thought of as for every 3 units of horizontal distance ($\Delta x = 3$), the vertical distance ($\Delta y$) changes by - 14 units. In other words, for every 3 feet of horizontal distance, the slide drops 14 feet. Equivalently, for every 14 feet of horizontal distance, the slide drops 3 feet.

Answer:

On average, the slide drops 3 feet for every 14 feet of horizontal distance.