1. **State the problem:** We want to find the slope $m$ of the line passing through the points $(2, -4)$ and $(5, 5)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" (change in $y$) over the "run" (change in $x$). 3. **Substitute the values:** Using the points $(2, -4)$ and $(5, 5)$, we have: $$m = \frac{5 - (-4)}{5 - 2}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{5 + 4}{3} = \frac{9}{3}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{9}}{\cancel{3}} \times \frac{3}{1} = 3$$ 6. **Interpretation:** The slope $m = 3$ means that for every 1 unit increase in $x$, the value of $y$ increases by 3 units. This is why the slope is 3. **Final answer:** $$m = 3$$