Given data:
The given equation of the line is y= 2x/3 -3.
The standard equation of the line is,
[tex]y=mx+c[/tex]
Compare the above equation with the given equation.
[tex]m=\frac{2}{3}[/tex]
The equation of the line perpendicular to the given line is,
[tex]\begin{gathered} y-b=-\frac{1}{(\frac{2}{3})}(x-a) \\ y-b=-\frac{3}{2}(x-a) \\ y=-\frac{3}{2}x+\frac{3a}{2}+b \end{gathered}[/tex]
Thus, the equation of the line perpendicular to the given line is y=-3x/2 +3a/2 +b.
