1. **Problem:** Determine the slope of the line passing through the points $(-4, 15)$ and $(2, 6)$. 2. **Formula:** The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the values:** $$m = \frac{6 - 15}{2 - (-4)} = \frac{6 - 15}{2 + 4} = \frac{-9}{6}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{ -9 }}{\cancel{6}} = -\frac{3}{2}$$ 5. **Interpretation:** The slope of the line is $-\frac{3}{2}$, which means the line falls 3 units vertically for every 2 units it moves horizontally to the right. **Final answer:** The slope of the line passing through $(-4, 15)$ and $(2, 6)$ is $-\frac{3}{2}$.