Find the equation of the line passes through midpoint A(2,4) and ( -1, -6) and parallel to the line 2y-4x - 8 = 0

To find the line through the mid point of A(2,4)  and B(-1,-6)
and parallel to 2y-2x-4.

The mid point of AB = M(x,y) = {(Ax+Bx)/2 ,
(Ay+By)/2} = {(2-1)/2 . (4-6)/2} = (1/2 ,-1).

Any line through
(x1,y1) = y-y1 = m(x-x1) where m is the slope of the line.

Since the
line through (1/2, -1) is parallel to 2y-4x-8 = 0, has the slope of 2y-4x-8 = 0 which is m =
-(coefficient of x)/(coefficient y) = -(-4)/2= 2.

Any line through
the mid point of AB = (1/2 , -1)  which is parallel to y has the slope = 2. So its equation
should be:

y - 1/2 = 2{x- -(-1)} =
2x+2

y-1/2 = 2x+2. We multiply this equation by
2:

 2(y -1/2) = 2(2x+2)

2y-2 =
4x+4.

2y-4x-2-4 = 0.

2y-4x -6 is
parallel to 2y -4x-8 and passes through (1/2, -1) , the mid point of A and
B.