Absolutely, unequivocally and in no uncertain terms it is just what it says, the path of the line. It's the job of everything else to maintain that linear path. I always teach to focus on the line verses the tip, which is tiny, fast and hard to guide on the other end of a flexing wand. The line however is long, slower in appearance, and the straightness of lack thereof is readily apparent.
For example, if the rod had zero flex, or if it was as soft as a noodle the caster must compensate motion to guide a given line in a straight line from the front end to the fly in order to make a tight loop. Either can do the job if the stop is compact and close to the line's path.
Stiff rods offer less of a stable feel for 'feel casters' like me in exchange for top-end power, but in some hands they are just the ticket. I prefer a sense of stable energy through the cast in order to best maintain that steering sensation, in other words a rod that has a sweet flex that is neither soft nor stiff. However in certain applications I am just as willing to deploy a pool cue as I am willing to go to a willow branch for Vermont brookies.
IFFF Certified THCI @ 2005
Capeflyfisher Guide Service
Island Hopper, Guitarist, Incurable Dreamer
and Founder, Worldwide Flyfishing Forum