You do need the slope. It's not obvious in "Standard Form".
Ax + By = C ==> y = -(A/B)x + (C/B)
There's your slope to compare. Find -A/B for each.
3x + 2y = 4 ==> Slope = -3/2
6x + 4y = 5 ==> Slope = -6/4 = -3/2
3x + y = 4 ==> Slope = -3
The top two examples COULD be parallel. If the constant is the same, that's a bit sneaky because they are really the SAME line. That's not really parallel.
