Find an equation of the line​ L, where L is perpendicular to y equals two thirds x and passes through the point ​(3​,2​).

Answer 1

y=(2/3)x

perpendicular line has the negative inverse of the given line's slope or -3/2

then use the point slope formula

y-h = -3(x-k)/2, with (h,k) = (3,2)

y-2 = -3(x-3)/2

2y-4 = -3x +9

3x+2y = 13 is the equation of a perpendicular line through the point (3,2)