Write an equation for a line perpendicular to 3y−6x=6 and passing through the point (4,-6)

Answer 1

Solve for y to find the slope of the line

3y-6x=6

3y=6x+6

y=2x+2

Since the slope of the line is 2, the slope of the line perpendicular will be the negative reciprocal, so -1/2

Set up an equation for a line with that slope

y=-1/2x+b

Solve for b using the given point (4,-6)

y=-1/2x+b

-6=-1/2(4)+b

-6=-2+b

-4=b

Then the equation for the perpendicular line is

y=-1/2x-4