Linear Functions with Two Points of Intersection?

Abstract

Of course two straight lines in Euclidean space cannot intersect in more than one point unless they are the same line and intersect everywhere—or can they? Follow this problem on the graphing calculator, however, and the surprising twist that gives this article its name will be seen. The material covered should be readily accessible to first-year-algebra students who have studied systems of equations, but it also contains valuable lessons for college mathematics professors who have been easily deceived by its apparent simplicity and familiarity.