The line-plane intersection can present three different scenarios:
If the line is parallel to the plane and doesn't intsersect it, then there are 0 points that belong to both line and plane
If the line intersects the plane, but it's not parallel to it, then there is 1 point belonging to both line and plane
If the line intersects the plane and they are parallel, then the entire line belongs to the plane, and there are infinitely many points belonging to both the line and the plane
