1. **State the problem:** We need to find the rate of change of the amount Miguel earns with respect to the hours he works. This is the slope of the line passing through the points (2, 26) and (5, 65). 2. **Formula for rate of change (slope):** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (2, 26)$ and $(x_2, y_2) = (5, 65)$. 3. **Calculate the difference in earnings and hours:** $$m = \frac{65 - 26}{5 - 2}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{39}{3}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{39}}{\cancel{3}} = 13$$ 6. **Interpretation:** The rate of change is 13 dollars per hour, meaning Miguel earns 13 dollars for every hour he works. **Final answer:** $$\boxed{13 \text{ dollars per hour}}$$