Geometry :: Example :: Cartesian Plane

Interpret point to be any ordered pair \((x,y)\) of real numbers. Interpret line as the collection of points which satisfy the equation \(ax+by+c = 0\), where \(a,b\) and \(c\) are real numbers and \(a\) and \(b\) are not both 0. Interpret incident as \((x_0,y_0)\) lies on a line if that point satisfies the lines equation. Show that this is a model for incidence geometry. We use \(\bbR^2\) to denote the set of points in this model.