Question

Find the equation of the line whose slope is 4/5 and which bisects te line joining the points P(1,2) and and Q(4,-3)

Answer 1

so the midpoint of P and Q is
x = (1+4)/2 = 5/2
y = (2 - 3)/2  = -1/2

so the mid point be Z(5/2,-1/2)

so the line is 

(y+1/2) = 4/5(x - 5/2)

⇒(2y + 1)/2 = 4/5(2x - 5)/2

⇒10y + 5 = 8x - 20

⇒8x - 10y - 25 = 0 ANSWER

Answer 2

given ,
slope of the equation = 4/5
and passing through the line of points p(1,2) and q(4,-3)
the line bisects it means passing through the mid point.
mid point of points p(1,2) and q(4,-3) is 
                                     [  (1+4)/2 , (2-3)/2 ]
                                   =( 5/2 , -1/2 )

so the line equation is ( y-y1 ) = m ( x-x1 )
                                 ( y+1/2 ) = 4/5 ( x-5/2 )
                                 (2y+1)/2  = 4/5 (2x-5)/2 
                                 (2y+1)/2 = (8x-20)/10
                                 (2y+1)5 = 8x-20
                                 10y+5 = 8x-20
                                 8x-10y-25=0