The discussion centers on the behavior of graphs representing Boyle's Law, specifically the graph of volume against 1/pressure and the graph of pressure against 1/volume. The first graph does not touch the starting point due to the mathematical relationship between volume and pressure, which indicates that as pressure approaches zero, volume approaches infinity. In contrast, the second graph touches the starting point because it represents a direct linear relationship where pressure increases as volume decreases. The difference in behavior is rooted in the inverse relationship described by Boyle's Law. Understanding these graphical representations is crucial for grasping the principles of gas behavior under varying pressure and volume conditions.