Question 53969
First solve the equation for y:  {{{y=2/3*x-2}}}.  That means the slope is {{{2/3}}} as the equation is the form y=mx+b, where m is the slope.  That also means that the slope of a line perpendicular to that one is {{{-3/2}}}.  So the equation of the line for the perpendicular becomes {{{y=-3/2*x+b}}}.  Using the ordered pair (0,2) gives us b=2, so our equation is now {{{y=-3/2*x+2}}}.  The graph of both equations is:
{{{graph(300,300,-5,5,-5,5,2x/3-2,-3x/2+2)}}}