2017 AMC 12A Problem 9

Let S be the 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 the common value. Which of the following is a correct description of S?

\begin{array}{l} \textbf{(A)}\ \text{a single point} \qquad\textbf{(B)}\ \text{two intersecting lines} \\ \qquad\textbf{(C)}\ \text{three lines whose pairwise intersections are three distinct points} \\ \qquad\textbf{(D)}\ \text{a triangle}\qquad\textbf{(E)}\ \text{three rays with a common point} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.