first, express the equation ins lope intercept form ( solve for y)
x-6y = -2
-6y = -x-2
y = (-x-2) /-6
y= 1/6x + 1/3
perpendicular line have negative inverse slopes:
slope = 1/6; negative inverse = -6
So far we have:
y= -6x +b
Replace (x,y) by the given point (-5,6) and solve for b (y intercept)
6 = -6(-5)+b
6 = 30+b
6-30= b
-24 = b
Final equation
y= -6x-24
