If the slope is the same but they have 2 different y-intercepts, the lines are parallel.
Remember that y=mx+b, where m is slope and b is y-int, y and x are variables.
Example:
y=3x+5 and y=3x+1
Parallel because the slope is the same.
y=3x-2 and y=2x-1
NOT parallel because the slope is different.
Hope that helps