Lines, Planes, and Hyperplanes

This section briefly summarizes the equations of lines and, by extension, hyperplanes. A line is a set of points that separates the Cartesian plane into two parts, a plane is a set of points that separates three-dimensional space into two parts, and, more generally, a hyperplane is the set of points that separates the space $\mathbb{R}^n$ into two parts. This definition will be useful later when classification is discussed.