The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

The point P has coordinates (3, 4) The point Q has coordinates (a, b)A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.
let l be the gradient for the perpendicular line
l = -1/m
m=(b-4)/(a-3)
l=-(a-3)/(b-4)
3x + 2y = 7
y= (7 - 3x)/2
l= -3/2
-3/2=-(a-3)/(b-4)
b-4= 2(a-3)/3
b=2(a-3)/3 +4