Lets write the given equation in the y = mx + c form y - 4 = -2/3(x-6) y - 4 = -2/3x + 4 y = -2/3x + 8 therefore the slope is -2/3 and intercept is +8 the perpendicular line passes through x = -2 and y = -2 then if the given graph has a slope of -2/3 the line that is perpendicular to that should have the reciprocal of the gradient and should be in the opposite direction. So m = +3/2 lets substitute x,y and m values for the new perpendicular line y =mx + c -2 = 3/2 * -2 +c -2 = -3 +c c = -2 +3 c = 1 Therefore the equation for the perpendicular line is y = 3/2x + 1
