Question 1071325
The perpendicular line has a slope that is the negative reciprocal of -3/5.  That would be +5/3
point slope formula 
y-y1=m(x-x1), where m is slope and (x1,y1) the point
y+2=(5/3)(x+3)
y=(5/3)x+3
-(5/3)x+y=3
multiply by -3
5x-3y=-9
That does go through (-3,-2)
{{{graph(300,300,-10,10,-10,10,(-3/5)x-5,(5/3)x+3)}}}