1.
Let:
[tex]\begin{gathered} (x1,y1)=(0,-4) \\ (x2,y2)=(2,-1) \\ so\colon \\ m1=\frac{y2-y1}{x2-x1}=\frac{-1-(-4)}{2-0}=\frac{3}{2} \end{gathered}[/tex]
Using the point-slope equation:
[tex]\begin{gathered} y-y1=m1(x-x1) \\ y-(-4)=\frac{3}{2}(x-0) \\ y+4=\frac{3}{2}x \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]
2.
If two lines are perpendicular, then:
[tex]\begin{gathered} m1\times m2=-1 \\ \frac{3}{2}\times m2=-1 \\ m2=-\frac{2}{3} \end{gathered}[/tex]
Let:
[tex](x1,y1)=(2,-1)[/tex]
Using the point slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-(-1)=-\frac{2}{3}(x-2) \\ y+1=-\frac{2}{3}x+\frac{4}{3} \\ y=-\frac{2}{3}x+\frac{1}{3} \end{gathered}[/tex]
