Lines, Planes, and Hyperplanes

This section provides a brief summary of the equations for lines and, by extension, hyperplanes. A line is a set of points that separates the Cartesian plane into two parts; the plane is the set of points that separates three-dimensional space into two parts, and, generalizing, the hyperplane is that set of points that separates space $\mathbb{R}^n$ into two parts. This definition will be useful when discussing classification later.