The equation of the line whose slope is 4/5 => y = 4x/5 + c
Line intersect at mid point of the line joining P(1,2) and and Q(4,-3).
Mid point of PQ = ((1+4)/2, (2-3)/2 )
=(5/2, -1/2)
The required line will pass through (5/2, -1/2)
-1/2 = 4(5/2)/5 + c
-1/2 = 2 + c
c = -5/2
y = 4x/5 -5/2
10 y = 8x - 25
The required equation of the line: 8x - 10y = 25.