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

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

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step-by-step explanation: