1. **State the problem:** Find the slope of the line passing through the points $(-2, 6)$ and $(-12, 2)$. 2. **Formula for slope:** The slope $m$ between two 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:** $$m = \frac{2 - 6}{-12 - (-2)} = \frac{2 - 6}{-12 + 2}$$ 4. **Simplify numerator and denominator:** $$m = \frac{-4}{-10}$$ 5. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2:** $$m = \frac{\cancel{-4}^{\div 2}}{\cancel{-10}^{\div 2}} = \frac{-2}{-5}$$ 6. **Simplify signs:** $$m = \frac{-2}{-5} = \frac{2}{5}$$ 7. **Final answer:** The slope of the line is $\boxed{\frac{2}{5}}$.