Parallel lines have the same slope. 4x-2y=9, so y=(4x-9)/2 making the slope 4/2=2.
The line we need looks like y=2x+a where a is what we have to find. Plug in (4,1):
1=8+a so a=-7 and y=2x-7.
Perpendicular lines have the negative inverse of the slope 2, so we have -1/2 as the slope.
y=-x/2+a where we have to find a different a this time. Plug in the given point:
1=-2+a so a=3 and the perpendicular line is y=-x/2+3 which can be written 2y=6-x.