1. **State the problem:** Find the equation of the line passing through the points $(-5, -6)$ and $(6, -3)$ in slope-intercept form $y=mx+b$. 2. **Formula for slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(-5,-6)$ and $(x_2,y_2)=(6,-3)$. 3. **Calculate the slope:** $$m=\frac{-3 - (-6)}{6 - (-5)}=\frac{-3 + 6}{6 + 5}=\frac{3}{11}$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Substitute $m=\frac{3}{11}$ and point $(-5,-6)$: $$y - (-6) = \frac{3}{11}(x - (-5))$$ $$y + 6 = \frac{3}{11}(x + 5)$$ 5. **Simplify to slope-intercept form:** $$y = \frac{3}{11}x + \frac{3}{11} \times 5 - 6$$ $$y = \frac{3}{11}x + \frac{15}{11} - 6$$ 6. **Convert 6 to fraction:** $$6 = \frac{66}{11}$$ 7. **Combine constants:** $$\frac{15}{11} - \frac{66}{11} = \frac{15 - 66}{11} = \frac{-51}{11}$$ 8. **Final equation:** $$y = \frac{3}{11}x - \frac{51}{11}$$ This is the fully simplified slope-intercept form of the line.