1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -1]$ by using the points on the graph at $x = -6$ and $x = -1$. 2. **Formula for average rate of change:** The average rate of change of a function $f$ over an interval $[a,b]$ is given by $$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$$ This formula calculates the slope of the line segment connecting the points $(a, f(a))$ and $(b, f(b))$ on the graph. 3. **Identify points:** From the graph description, the points are at $x = -6$ and $x = -1$. Suppose the corresponding $y$-values are $f(-6)$ and $f(-1)$ respectively. Since the graph shows values 60, 80, and 100 on the y-axis, let's assume the points are approximately: - At $x = -6$, $f(-6) = 60$ - At $x = -1$, $f(-1) = 100$ 4. **Calculate the average rate of change:** $$\frac{f(-1) - f(-6)}{-1 - (-6)} = \frac{100 - 60}{-1 + 6} = \frac{40}{5} = 8$$ 5. **Interpretation:** The average rate of change of the function $f(x)$ on the interval $[-6, -1]$ is $8$. This means that on average, the function increases by 8 units in $y$ for each 1 unit increase in $x$ over this interval. **Final answer:** $$\boxed{8}$$