Question

Find an equation of the line that passes through the point (9,2) and is perpendicular to the line 2x + 3y + 5 = 0.

Answer 1

y=3/2x-1 2/3

Answer 2

see for perpendicular you have condition that product of slopes of two line must be equal to -1. so as you are provided with slope of given line i.e. -2/3.so the slope of perpendicular line is 3/2.
now the let's take the equation perpendicular line y = mx+b ....put (9,2)in place of x and y since it satisfy the given as it is passing through that point and also we have found above that slope m = 3/2.
so noe u can get value of constant b . i.e -23/2
so finally eqn. of line is