1. **State the problem:** We are given a table showing the relationship between miles traveled $x$ and gallons of gas used $y$. We need to find the equation that best represents this relationship. 2. **Analyze the table:** \begin{align*} x &: 35, 70, 105, 140, 175 \\ y &: 1, 2, 3, 4, 5 \end{align*} 3. **Find the pattern:** Notice that as $x$ increases by 35, $y$ increases by 1. This suggests a linear relationship of the form: $$y = mx$$ where $m$ is the slope (gallons per mile). 4. **Calculate the slope $m$:** $$m = \frac{\text{change in } y}{\text{change in } x} = \frac{2 - 1}{70 - 35} = \frac{1}{35}$$ 5. **Write the equation:** $$y = \frac{1}{35}x$$ 6. **Check the options:** - A. $35 = 1x$ (incorrect, units reversed) - B. $y = 35x$ (incorrect, slope too large) - C. $y = 3.5x$ (incorrect, slope too large) - D. $y = \frac{1}{35}x$ (correct) **Final answer:** $$\boxed{y = \frac{1}{35}x}$$