1. **State the problem:** We need to find the rate of change of Tristan's earnings, which is the slope of the line passing through the points $(10, 248)$ and $(20, 496)$. 2. **Formula for rate of change (slope):** The rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ This represents how much $y$ changes for each unit change in $x$. 3. **Substitute the given points:** $$\text{slope} = \frac{496 - 248}{20 - 10}$$ 4. **Calculate the numerator and denominator:** $$\text{slope} = \frac{248}{10}$$ 5. **Simplify the fraction:** $$\text{slope} = 24.8$$ 6. **Interpretation:** The rate of change is $24.8$ dollars per hour, meaning Tristan earns $24.8$ dollars for each hour worked. **Final answer:** $$\boxed{24.8 \text{ dollars per hour}}$$