Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
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No. They could be parallel.
They may also be parallel lines.
No, never. Parallel lines are line that will NEVER intersect.
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
In Euclidian geometry, which is the geometry of a plane surface, parallel lines do not intersect because that is the definition of parallel lines. But note that there are other geometrical systems in which parallel lines do intersect, for example if they are drawn on the surface of a sphere. Definition of parallel lines: Lines that always stay the same distance apart and never meet.