Given a line, there are an infinite number of different planes that it lies in.
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If 2 points determine a line, then a line contains infinitely many planes.
There's no limit to the number of them. A more cool and sexy way to say the same thing might be: "An infinite number."
Anything that contains the line must contain every point on the line, so "a point on the line" doesn't give us any more information. You're just asking how many planes can contain the line. Now imagine setting a wood panel down on a tight-rope. How many different ways can it set there before it falls off ? A lot, right ? An infinite number of planes can all contain your line. (And all of its points.)
an infinite number; no limit
No, they intersect at a line.