Pick several points on this line (on the "object" side of the picture plane), and draw the lines of sight from the viewer's eye to the those points. What can you say about what happens to the perspective images of these points as the original points get farther and farther away from the viewer?
Note: To get a better idea of what's going on, you may find it helpful to draw a top view and a side view of what's going on, similar to what we did to develop the perspective theorem in the first place.