Theorem 7.2: Each point in an affine plane of order [math]k[/math] lies on [i][math]k+1[/math][/i] lines. [br][br]Proof: Let [math]l_1[/math] be an arbitrary line. By Theorem 7.1, we know that [math]l_1[/math] has k points. Let [i]p[/i] be an arbitrary point not on [math]l_1[/math]. By Axiom 2, every point on [math]l_1[/math] must have exactly one line in common with [i]p[/i]. By Axiom 3, [i]p[/i] has exactly one line parallel to [math]l_1[/math]. [br][br]Therefore, any point in an affine plane of order [math]k[/math] has [math]k+1[/math] lines.