First, take into account that the general form of a linear equation is:
y = mx + b
where m is the slope and b the y-intercept.
When two lines are parallel, their slopes are equal.
When two lines are perpendicular, you can verify the following relation between slopes:
m1 = -1/m2
Then:
A)
y = 4x - 9
y + 4x = 3 which is the same as
y = -4x + 3
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
B)
y = 3x + 7
y + 2 = 3(x-5) which is the same as
y = 3x - 15 - 2
y = 3x - 17
In this case the slopes are the same, then, the lines are parallel
C)
y = 2x
2y = x - 9 which is the same as
y = 1/2 x - 9/2
In this case you can notice that the slopes are not the same and m1 ≠ -1/m2.
Hence, the lines are not neither parallel nor perpendicular.
D)
y + x = 0 which is the same as
y = -x
y = x
In this case you can verify that m1 = -1/m2, then, the line are perpendicular.