1. **State the problem:** Find the slope of the line passing through the points $(-6, -12)$ and $(8, -14)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the "rise" (change in $y$) over the "run" (change in $x$). 3. **Identify the coordinates:** Here, $x_1 = -6$, $y_1 = -12$, $x_2 = 8$, and $y_2 = -14$. 4. **Calculate the difference in $y$-values:** $$y_2 - y_1 = -14 - (-12) = -14 + 12 = -2$$ 5. **Calculate the difference in $x$-values:** $$x_2 - x_1 = 8 - (-6) = 8 + 6 = 14$$ 6. **Write the slope as a fraction:** $$m = \frac{-2}{14}$$ 7. **Simplify the fraction by dividing numerator and denominator by 2:** $$m = \frac{\cancel{-2}}{\cancel{14}} = \frac{-1}{7}$$ 8. **Interpretation:** The slope of the line through the points $(-6, -12)$ and $(8, -14)$ is $-\frac{1}{7}$. This means for every 7 units you move to the right, the line goes down by 1 unit. **Final answer:** $$\boxed{-\frac{1}{7}}$$