They can be any distance apart
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Parallel lines are equidistant from one another
Lines that are equal distance from one another and never intersect are said to be parallel lines.
Parallel lines stay a fixed distance apart to infinity.
It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.
Parallel lines are lines that share the same slope (number in front of the x) In this case you need two lines that have 2x to be considered parallel to one another.