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Kelly and Moser prove that $f(n)\ge 3n/7$ for every $n$: $n$ points in the real plane, not all on one line, determine at least $3n/7$ ordinary lines, lines through exactly two of the points. The bound is attained at $n=7$. The proof works in the dissection of the plane by the lines not through a given point; the source card [[../library/discrete_geometry/kelly_1958_number_ordinary_lines_determined_points/_index|records the statement as Theorem 3.6]] together with Dirac's conjecture, restated in the paper, that $f(n)\ge n/2$ for $n>7$, which fails at $n=13$ (Crowe and McKee). The result is the first linear lower bound for Problem 210.

Covers. A linear lower bound valid for every $n$, with the constant $3/7$. It does not give the sharp constant, which Green and Tao later determine for large $n$.

The result is refereed: L. M. Kelly and W. O. J. Moser, On the number of ordinary lines determined by $n$ points, Canadian J. Math. 10 (1958), 210-219. The site's page credits this paper with the bound $3n/7$; its label, proved, rests on the later results, so the acceptance here stands on the refereed publication.