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.
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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.
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 the lines are straight and have the same slope they are parallel, no matter what the y intercept is
Lines with equal slopes are parallel, because they are going the same direction. If the slope and the intercept are the same, the lines are coinciding, because they are on top of each other.
It is a transversal line