1. **State the problem:** Find the slope of the line passing through the points $(-6, 0)$ and $(-3, -3)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. **Substitute the points:** Here, $(x_1, y_1) = (-6, 0)$ and $(x_2, y_2) = (-3, -3)$. So,\n$$m = \frac{-3 - 0}{-3 - (-6)} = \frac{-3}{-3 + 6} = \frac{-3}{3}$$\n\n4. **Simplify the fraction:**\n$$m = \frac{\cancel{-3}}{\cancel{3}} \times \frac{-1}{1} = -1$$\n\n5. **Interpretation:** The slope of the line is $-1$, which means the line falls one unit vertically for every one unit it moves horizontally to the right.