AMC 10 2017a Problem 12

Let $S$ be a set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3,~x+2,$ and $y-4$ are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for $S?$ $\textbf{(A)}\ \text{a single point} \textbf{(B)}\ \text{two intersecting lines} \\ \textbf{(C)}\ \text{three lines whose pairwise intersections are three distinct points} \\ \textbf{(D)}\ \text{a triangle} \textbf{(E)}\ \text{three rays with a common endpoint}$