1. **State the problem:** Find the slope of the line passing through the points $(-8, -4)$ and $(4, 2)$ on the coordinate plane. 2. **Formula for slope:** The slope $m$ of a line 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 given points:** $$m = \frac{2 - (-4)}{4 - (-8)}$$ 4. **Simplify the numerator and denominator:** $$m = \frac{2 + 4}{4 + 8} = \frac{6}{12}$$ 5. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 6:** $$m = \frac{\cancel{6}^1}{\cancel{12}^2} = \frac{1}{2}$$ 6. **Interpretation:** The slope of the line is $\frac{1}{2}$, meaning for every 2 units moved horizontally, the line rises 1 unit vertically. **Final answer:** $$m = \frac{1}{2}$$