That hose goes to the air valve which is under the seat, just in front of the battery. It has another hose coming off it that goes to the rear cylinder as well, but on the left side of the bike.
Those are the hoses that get "marbled" or removed and "coastered", both are well known around here and are done usually to reduce/eliminate the popping heard from the mufflers on deceleration.
The valve and those hoses are emissions parts.
If you look in the Verses, or do a search for those terms I mentioned, you can read more details on each.
If you decide you just want to replace the hose regardless, let me know before tomorrow, and I'll throw one in with the footpeg.
Here's a pic of what we're talking about. The assembly in the center of the drawing is the air valve, (item #16126) with the hose's coming off of it. One to each cylinder, one to the air box, and a small one to the right side carb.
#92059B is the hose you're asking about. This diagram is from Bike Bandit.