1. **State the problem:** Find the slope of the line passing through the points $(-5, 0)$ and $(0, 2)$. 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 points:** Here, $x_1 = -5$, $y_1 = 0$, $x_2 = 0$, and $y_2 = 2$. So, $$m = \frac{2 - 0}{0 - (-5)} = \frac{2}{0 + 5}$$ 4. **Simplify the denominator:** $$m = \frac{2}{5}$$ 5. **Interpretation:** The slope of the line is $\frac{2}{5}$. This means for every 5 units moved horizontally to the right, the line rises 2 units vertically. **Final answer:** $$m = \frac{2}{5}$$