If two lines do not intersect, are they parallel?

Question

This is a very hard question. 

Answer 1

If two lines in a plane do not intersect, they are parallel.

If two lines in space and not in the same plane do not intersect, they are skew.

Answer 2

The answer is yes. Two lines can only be non-intersecting if their slopes are exactly the same (otherwise they'd have to cross at some point). So if two lines have the same slope, then they are always moving in lock step with each other.  If one rises by x, then the other rises by x too. So the two lines can only be parallel because they never cross and move with the same slope.