1. **State the problem:** Find the equation of the line passing through the points $(-8,8)$ and $(8,-4)$ 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 $(x_1,y_1)=(-8,8)$ and $(x_2,y_2)=(8,-4)$. 3. **Calculate the slope:** $$m=\frac{-4 - 8}{8 - (-8)}=\frac{-12}{8+8}=\frac{-12}{16}$$ 4. **Simplify the slope:** $$m=\frac{\cancel{-12}}{\cancel{16}}=\frac{-3}{4}$$ 5. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Substitute $m=-\frac{3}{4}$ and point $(-8,8)$: $$y - 8 = -\frac{3}{4}(x - (-8))$$ $$y - 8 = -\frac{3}{4}(x + 8)$$ 6. **Distribute the slope:** $$y - 8 = -\frac{3}{4}x - \frac{3}{4} \times 8$$ $$y - 8 = -\frac{3}{4}x - 6$$ 7. **Solve for $y$ to get slope-intercept form:** $$y = -\frac{3}{4}x - 6 + 8$$ $$y = -\frac{3}{4}x + 2$$ **Final answer:** The equation of the line in slope-intercept form is $$y = -\frac{3}{4}x + 2$$.