Then you have a number line with two points labelled on it.
any given line can have an infinite number of possible points.
Yes. Even the shortest line has an infinite number of points.
A line is made up of an infinite number of points.
Real Number line
A Number Line
where is 8.5 on a number line
4 is one of infinitely many points on a number line. There is not a special number line for 4!
Only two points.
In Euclidean geometry each line contains a minimum of an infinite number of points. In projective geometry, though, a line may have as few as two points.