For a line to be perpendicular to a reference line, it must have a slope that is the negative reciprocal of the reference line's slope, mathematically:
m1*m2=-1, where m1 and m2 are the slopes of the perpendicular lines for them to be perpendicular. In this case, the slope of the reference line is 3/4 so:
3m/4=-1
3m=-4
m=-4/3
So the perpendicular line will have a slope of -4/3, then the line is currently:
y=-4x/3+b, we can solve for b using the point that we must pass through.
-2=-4(-6)/3+b
-2=8+b
-10=b, so our perpendicular line is:
y=-4x/3-10 or more neatly in my opinion:
y=(-4x-30)/3