No, parallel lines never meet or cross each other.
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Unless they are the exact same lines, no. Parallel lines do not touch. If two lines have the same intercept value, they share a point, and therefore touch.
Skew lines are lines that lie on separate planes. and do not intercept parallel lines that are sometimes on the same plane, but don't intersect
If parallel lines had the same y intercept then they would intersect each other at that point (0, c). Parallel lines don't intersect at all so they cannot have the same y intercept. The only exception would be if both lines were the same.
If the lines are straight and have the same slope they are parallel, no matter what the y intercept is
In plain geometry, if 2 lines never intersect, they are Parallel