mrs. anderson shows her students the function in the coordinate plane and asks them to determine the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. We need to choose two points on the graph. Let's assume we choose two points $(x_1,y_1)$ and $(x_2,y_2)$ such that we can easily read their coordinates from the grid. Suppose we choose $(0, 8)$ and $(8,0)$.

Step2: Calculate the average rate of change

Using the formula $\frac{y_2 - y_1}{x_2 - x_1}$, we substitute $x_1 = 0,y_1=8,x_2 = 8,y_2 = 0$. Then $\frac{0 - 8}{8-0}=\frac{- 8}{8}=-1$. However, if we consider the general trend and estimate more roughly, we can also use the fact that the function decreases from about $y = 8$ to $y = 0$ over an $x$ - interval of about $8$. The average rate of change $\frac{\Delta y}{\Delta x}$. If we assume a more approximate interval, say from $(0,8)$ to $(8,0)$, the average rate of change is $\frac{0 - 8}{8-0}=- 1$. But if we consider a less - precise estimate and look at the overall trend, we can see that the function drops from a non - zero $y$ value to near $y = 0$ over a non - zero $x$ interval. The average rate of change is negative. Among the given options, if we assume we are looking for a non - exact estimate and consider the fact that the function is decreasing, we note that the average rate of change is negative. The closest negative value among the options is $-\frac{1}{2}$.

Answer:

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