Parallel lines are lines in a plane that are always the same distance apart.
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Lines with the same slope that never touch each other.
Parallel lines share the same slope (direction). Attached is an example of two lines parallel to each other, in red and in green. They both have a slope of , which is what makes them parallel.
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in red and 
in green. They both have a slope of 
, which is what makes them parallel.