1. **State the problem:** We are given miles run and calories burned and asked if calories are proportional to miles, find calories burned for 7.5 miles, find the constant of proportionality, and write an equation relating miles and calories. 2. **Check proportionality:** Two quantities are proportional if their ratio is constant. Calculate $\frac{\text{Calories}}{\text{Miles}}$ for given data: $$\frac{117}{1} = 117, \quad \frac{234}{2} = 117, \quad \frac{351}{3} = 117, \quad \frac{468}{4} = 117, \quad \frac{585}{5} = 117$$ Since the ratio is constant at 117, calories burned is proportional to miles run. 3. **Find calories burned for 7.5 miles:** Use the constant of proportionality $k=117$: $$\text{Calories} = k \times \text{Miles} = 117 \times 7.5 = 877.5$$ 4. **Constant of proportionality:** From step 2, $k = 117$. 5. **Write the equation:** Let $C$ be calories burned and $m$ be miles run: $$C = 117m$$ **Summary:** Calories burned is proportional to miles run with constant $117$. For 7.5 miles, calories burned is $877.5$. The equation is $C=117m$.