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It is also known as the Cartesian plane where shapes and lines are plotted on it.
If you mean the plural of plane, it is planes. If you mean the spelling of another word that is pronounced the same way, it is plain.
If you mean "plane", then yes it is.
you mean inclined plane? a simple machine (a plane at an incline) that uses gravity and slope to move objects. e.g.: a slide is an inclined plane. If it were horizontal, you wouldn't go anywhere.
If they are in the same plane, then they share a common plane. Did you mean to say common point. If that's the case where they are in the same plane, but do not share a common point, then they are parallel lines.