Question

I have to write an equation for the line that passes through the given point and is perpendicular to the graph of the given equation

Answer 1

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