2024 AMC 8 Problem 23

Rodrigo has a very large piece of graph paper. First he draws a line segment connecting point (0, 4) to point (2, 0) and colors the 4 cells whose interiors intersect the segment, as shown below. Next, Rodrigo draws a line segment connecting point (2000, 3000) to point (5000, 8000). Again he colors the cells whose interiors intersect the segment. How many cells will he color this time?

\textbf{(A)} 6000 \qquad \textbf{(B)} 6500 \qquad \textbf{(C)} 7000 \qquad \textbf{(D)} 7500 \qquad \textbf{(E)} 8000

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