1. **State the problem:** Find the equation of the line passing through the points $(-4, 6)$ and $(-2, 0)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line in point-slope form is $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope:** $$m = \frac{0 - 6}{-2 - (-4)} = \frac{0 - 6}{-2 + 4} = \frac{-6}{2} = -3$$ 4. **Write the equation using point-slope form with point $(-4, 6)$:** $$y - 6 = -3(x - (-4))$$ $$y - 6 = -3(x + 4)$$ 5. **Simplify the equation:** $$y - 6 = -3x - 12$$ $$y = -3x - 12 + 6$$ $$y = -3x - 6$$ 6. **Final answer:** The equation of the line is $$\boxed{y = -3x - 6}$$