1. **State the problem:** We are given a table showing miles traveled ($x$) and total cost ($y$). We want to find the rate of change, which is the slope of the linear relationship between $x$ and $y$. 2. **Formula:** The rate of change (slope) $m$ is given by the formula: $$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points from the table. 3. **Choose two points:** Let's use the first two points: $(5, 16)$ and $(15, 44)$. 4. **Calculate the change in $y$ and $x$:** $$\Delta y = 44 - 16 = 28$$ $$\Delta x = 15 - 5 = 10$$ 5. **Calculate the slope:** $$m = \frac{28}{10}$$ 6. **Simplify the fraction:** $$m = \frac{\cancel{28}^{14 \times 2}}{\cancel{10}^{5 \times 2}} = \frac{14}{5} = 2.8$$ 7. **Interpretation:** The rate of change is $2.8$, meaning the total cost increases by 2.8 units for each additional mile traveled. **Final answer:** The rate of change is $2.8$ per mile.