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

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