The point *P *has coordinates (3, 4) The point *Q *has coordinates (*a*, *b*)A line perpendicular to PQ* *is given by the equation 3*x *+ 2*y *= 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