1. The problem asks to calculate the slope (rate of change) of shoe size with respect to height. 2. The slope formula is $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ where $y$ is shoe size and $x$ is height in inches. 3. From the graph, approximate two points: $(0,1)$ and $(80,8)$. 4. Calculate the slope: $$\text{slope} = \frac{8 - 1}{80 - 0} = \frac{7}{80} = 0.0875$$ 5. This means shoe size increases by 0.0875 units for every 1 inch increase in height. 6. The problem states shoe size decreases by 6 every 80 inches, so the rate of change is $$\frac{-6}{80} = -0.0750$$. 7. Since the graph shows an increase, the slope is positive $0.0875$, but the problem states a decrease, so the slope (rate of change) is $$-0.0750$$ rounded to four decimal places. Final answer: rate of change = $-0.0750$