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Algebra: If given two equations of a line, then you can assume that they are in the same plain. If the two slopes are equal, then the lines are parallel.

Geometry: If given two lines in the same plane that never intersect, then these two lines are parallel. If the lines are in different planes, but never intersect, then the lines are skew.

So, both definitions use lines and a plane. The answer is yes.

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Q: Are a line and a plain are needed to define parallel lines?
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