first you need to find the slope. Solve them for y.
x+4y =7
4y = -x + 7
y = -1/4x +7/4 Slope is -1/4
4x-y=3
-y = -4x + 3
y = 4x - 3 Slope is 4
They are perpendicular because -1/4 is the negative reciprical of 4 (flip the top and bottom and change the sign)