The postulate that pertains to a line is:
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converse of the corresponding angles postulate
euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.
This is Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
Euclid's second postulate allows that line segment to be extended farther in that same direction, so that it can reach any required distance. This could result in an infinitely long line.
If two points are in a plane, then the line that contains the points is in that plane