2017 AMC 10A 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?

\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 endpoint} \end{array}

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