[tex]\begin{gathered} P1(2,-2) \\ P2(0,1) \\ y=mx+b \\ m=\frac{y2-y1}{x2-x1} \\ m=\frac{1-(-2)}{0-2}=\frac{1+2}{-2}=\frac{-3}{2} \\ y=-\frac{3}{2}x+b \\ P2(0,1) \\ 1=\frac{-3}{2}(0)+b \\ 1=0+b \\ b=1 \\ y=-\frac{3}{2}x+1 \\ \text{The linear equation is }y=-\frac{3}{2}x+1 \\ \\ 6. \\ P1(1,3) \\ P2(-3,-5) \\ m=\frac{-5-3}{-3-1}=\frac{-8}{-4}=2 \\ y=2x+b \\ U\sin g\text{ point 1} \\ 3=2(1)+b \\ 3=2+b \\ 3-2=b \\ b=1 \\ y=2x+1 \\ \text{The linear equation is }y=2x+1 \\ \\ 8. \\ P1(3,3) \\ P2(1,-3) \\ m=\frac{-3-3}{1-3}=\frac{-6}{-2}=3 \\ y=3x+b \\ U\sin g\text{ point 1} \\ 3=3(3)+b \\ 3=9+b \\ 3-9=b \\ b=-6 \\ y=3x-6 \\ \text{The linear equation is }y=3x-6 \\ \\ 10. \\ P1(-1,4) \\ P2(0,-1) \\ m=\frac{-1-4}{0-(-1)}=\frac{-5}{1}=-5 \\ y=-5x+b \\ U\sin g\text{ point 2} \\ -1=-5(0)+b \\ -1=0+b \\ b=-1 \\ y=-5x-1 \\ \text{The linear equation is }y=-5x-1 \end{gathered}[/tex]
