1. **State the problem:** Find the slope $m$ of the line passing through the points $(-34, 80)$ and $(-60, 21)$. 2. **Formula for slope:** The slope 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 given points:** $$m = \frac{21 - 80}{-60 - (-34)}$$ 4. **Simplify numerator and denominator:** $$m = \frac{-59}{-60 + 34} = \frac{-59}{-26}$$ 5. **Cancel negatives:** $$m = \frac{\cancel{-59}}{\cancel{-26}} = \frac{59}{26}$$ 6. **Final answer:** The slope of the line is $$m = \frac{59}{26}$$ This fraction is already in simplest form.