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A point has an infinite amount of lines passing through it.
Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
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.
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
In Geometry