Yes - except in finite geometries (projective, for example).
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an infinite number
an infinite number; no limit
It is possible to construct an infinite number of lines through any line at a given point. You will not be able to physically draw them, but a filled in circle will all have rays that intersect the line at the same point.
A line is made up of a large (infinite) number of points. When we say a point is on a line, we mean that it is one of the pints that form the line.
Infinitely many. There an infinite number of points on a line and each point can be an end point of two rays.