2023 AMC 8 Problem 7

A rectangle, with sides parallel to the x-axis and y-axis, has opposite vertices located at (15, 3) and (16, 5). A line is drawn through points A(0, 0) and B(3, 1). Another line is drawn through points C(0, 10) and D(2, 9). How many points on the rectangle lie on at least one of the two lines?

\textbf{(A)} 0 \qquad \textbf{(B)} 1 \qquad \textbf{(C)} 2 \qquad \textbf{(D)} 3 \qquad \textbf{(E)} 4

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