Determine the equation of the line that is perpendicular to 2x−3y+6=0 and passes through the point (4, -2).

Question

(1 mark for identifying correct perpendicular slope, 1 mark for substituting values correctly into equation, 1 mark for isolating and solving for b, 1 mark for creating correct equation)

Answer 1

2x-3y + 6 = 0

3y = 2x + 6

y = 2x/3 + 2

slope = 2/3, slope of perpendicular line is the negative inverse: -3/2

y=(-3/2)x + b, plug in (4,-2)

-2 = (-3/2)4 + b

b = -2 +6 = 4

y= (-3/2)x + 4

or

2y = -3x + 8

3x+2y = 8 is perpendicular going through (4,-2)