Given an arrangement of points, a Line containing just two of them is called an ordinary line. Moser (1958) proved that at least lines must be ordinary (Guy 1989, p. 903).
See also General Position, Near-Pencil, Ordinary Point, Special Point, Sylvester Graph
Guy, R. K. ``Unsolved Problems Come of Age.'' Amer. Math. Monthly 96, 903-909, 1989.