[spldart]

On the side of the carb closer to the engine there is a small tube. If you pull the tank and seat,
sit on the bike and pretend you can see through the frame it faces up and to the left.
A small vacuum line fits from there to the back of the petcock.
It's real close to the engine side carb clamp. Not the airbox side.
If a shop missed this then they weren't very thorough.
However. If your talking the typical safety inspection for your typical DOT then they wouldn't know better.

edit: and the bike runs fine with this line missing in prime? did someone plug the fitting at the carb?
Normally this hose being missing and no plug on the fitting at the carb would mess with idle.