Rodrigo draws a segment from $(0,3)$ to $(4,0)$ and colors the 6 unit cells whose interiors the segment passes through, as shown. He then draws a segment from $(0,0)$ to $(4000,6000)$. Through the interiors of how many unit cells does this new segment pass?
罗德里戈先画一条从 $(0,3)$ 到 $(4,0)$ 的线段，把它内部穿过的 6 个方格涂色（如图）。接着他画一条从 $(0,0)$ 到 $(4000,6000)$ 的线段。这条新线段内部穿过多少个方格？