1. **State the problem:** We need to estimate the average rate of change of money spent on fuel with respect to average speed from $x=5$ to $x=9$. 2. **Recall the formula for average rate of change:** $$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$$ where $a=5$, $b=9$, $f(a)$ and $f(b)$ are the money spent at speeds 5 and 9 respectively. 3. **Identify the points from the graph:** At $x=5$, $f(5) = 7$ dollars. At $x=9$, $f(9) = 10$ dollars. 4. **Calculate the average rate of change:** $$\frac{f(9) - f(5)}{9 - 5} = \frac{10 - 7}{9 - 5} = \frac{3}{4}$$ 5. **Simplify the fraction:** $$\frac{\cancel{3}}{\cancel{4}} = 0.75$$ 6. **Interpretation:** The average rate of change is 0.75 dollars per mile per hour, meaning for each 1 mph increase in speed above 40 mph, the money spent on fuel increases by approximately 0.75 dollars between speeds 5 and 9 mph above 40 mph. **Final answer:** $$\boxed{0.75}$$