1. **Problem Statement:** Find the slope, y-intercept, and equation of the line for each graph. 2. **Formula for slope:** $$m=\frac{y_2-y_1}{x_2-x_1}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. 3. **Equation of a line:** $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. --- ### a) Line passing through points $(-4,-2)$ and $(8,8)$ 4. Calculate slope: $$m=\frac{8-(-2)}{8-(-4)}=\frac{8+2}{8+4}=\frac{10}{12}$$ 5. Simplify slope: $$m=\frac{\cancel{10}}{\cancel{12}}=\frac{5}{6}$$ 6. Find y-intercept $b$ by substituting slope and one point into $y=mx+b$: Using point $(-4,-2)$: $$-2=\frac{5}{6}(-4)+b$$ $$-2=-\frac{20}{6}+b$$ $$b=-2+\frac{20}{6}=-2+\frac{10}{3}$$ 7. Convert $-2$ to fraction: $$-2=\frac{-6}{3}$$ 8. Add fractions: $$b=\frac{-6}{3}+\frac{10}{3}=\frac{4}{3}$$ 9. Equation of the line: $$y=\frac{5}{6}x+\frac{4}{3}$$ --- ### b) Line passing through points $(-4,6)$ and $(8,-2)$ 10. Calculate slope: $$m=\frac{-2-6}{8-(-4)}=\frac{-8}{12}$$ 11. Simplify slope: $$m=\frac{\cancel{-8}}{\cancel{12}}=\frac{-2}{3}$$ 12. Find y-intercept $b$ by substituting slope and one point into $y=mx+b$: Using point $(-4,6)$: $$6=\left(-\frac{2}{3}\right)(-4)+b$$ $$6=\frac{8}{3}+b$$ $$b=6-\frac{8}{3}$$ 13. Convert $6$ to fraction: $$6=\frac{18}{3}$$ 14. Subtract fractions: $$b=\frac{18}{3}-\frac{8}{3}=\frac{10}{3}$$ 15. Equation of the line: $$y=-\frac{2}{3}x+\frac{10}{3}$$