Although the phase plane can be plotted and analyzed using an appropriate software package, the author found it worthwhile to engage the students with the theorem and the two proofs. The theorem is a powerful tool that provides insight into the rotational behavior of the phase plane diagram in a simple way: just check the signs of c and [alpha]. The student is then better prepared to make sense of what the software is presenting them. The theorem can also be extended to the case of one repeated eigenvalue with one independent eigenvector (and, in addition, a generalized eigenvector), a case also displaying rotational behavior save for one straight line solution. (Contains 2 figures.)