1. **Problem Statement:** We are given a line segment from point $(-9,4)$ to point $(9,-6)$ on the Cartesian plane. We need to find the "rise" and "run" of the line and then calculate the slope in simplest form. 2. **Formula for slope:** The slope $m$ of a line passing 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 represents the "rise" (change in $y$) over the "run" (change in $x$). 3. **Calculate rise and run:** - Rise $= y_2 - y_1 = -6 - 4 = -10$ - Run $= x_2 - x_1 = 9 - (-9) = 9 + 9 = 18$ 4. **Express slope:** $$m = \frac{-10}{18}$$ 5. **Simplify the fraction:** Both numerator and denominator can be divided by 2: $$m = \frac{\cancel{2} \times (-5)}{\cancel{2} \times 9} = \frac{-5}{9}$$ 6. **Interpretation:** The slope of the line is $-\frac{5}{9}$. This means for every 9 units moved horizontally to the right (run), the line goes down 5 units (rise). 7. **Summary:** - Rise: $-10$ - Run: $18$ - Simplified slope: $-\frac{5}{9}$ This slope is negative, indicating the line descends from left to right.