1. **State the problem:** Find the slope of the line passing through the points $(-3, 12)$ and $(-11, 2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" over the "run" or the change in $y$ divided by the change in $x$. 3. **Substitute the given points:** $$m = \frac{2 - 12}{-11 - (-3)}$$ 4. **Simplify numerator and denominator:** $$m = \frac{-10}{-11 + 3}$$ 5. **Simplify the denominator:** $$m = \frac{-10}{-8}$$ 6. **Cancel common negative signs:** $$m = \frac{\cancel{-}10}{\cancel{-}8} = \frac{10}{8}$$ 7. **Simplify the fraction:** $$m = \frac{10 \div 2}{8 \div 2} = \frac{5}{4}$$ **Final answer:** The slope of the line passing through $(-3, 12)$ and $(-11, 2)$ is $\boxed{\frac{5}{4}}$.