Problem 7 (2023 AMC 8)

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? [See figure in original PDF]