1. **State the problem:** Find the slope $m$ of the line passing through the points $(-5,12)$ and $(9,-10)$ in the form $y=mx+b$. 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:** Here, $x_1=-5$, $y_1=12$, $x_2=9$, and $y_2=-10$. So, $$m=\frac{-10 - 12}{9 - (-5)}$$ 4. **Simplify numerator and denominator:** $$m=\frac{-22}{9 + 5}$$ 5. **Add in denominator:** $$m=\frac{-22}{14}$$ 6. **Simplify the fraction by dividing numerator and denominator by 2:** $$m=\frac{\cancel{-22}^{\div 2}}{\cancel{14}^{\div 2}}=\frac{-11}{7}$$ 7. **Final answer:** The slope of the line is $m=-\frac{11}{7}$.