Hi all,
This line is filthy inside, it runs down to the front of the case on the foot brake side. Is it supposed to connect somewhere under the tank?

 

That is your crankcase blow-by hose. It goes into the hole in the snorkel tube to recirculate the blow-by into the airbox to be filtered before being sucked back into the motor via the carb.

 

I took the tank off. There seems to be nothing to connect to. What is the point of the white clip on it? What do you mean by "The hole in the snorkel tube"? Thanks for the reply.

 

If you look at the picture you posted those two tubes that you took out from under the tank cover are the snorkels that run back in to the airbox. The one pictured on the left has a hole in it. The blow-by hose goes in to that hole up to the white clip. The clip just kinda holds it back from the opposite side of the snorkel to allow it to breathe.
Lots of post on here where folks have put a K&N type filter on that hose. Most of those have completely removed the airbox and snorkels altogether. If you ride in mud and water leave the box, if you ride primarily sand and desert then shed the extra weight.

 

every engine must have a crankcase breather, otherwise the crankcase would be under vacuum when piston goes up, and under pressure when it goes down, not to mention the bit of combustion blowby around the piston during firing.

back in the old days crankcase breathers used to simply be a rubber tube going down to the ground, but somewhere along the line emmisions control standards dictated that the breather must go to the intake system so that any emmisions vapors would be burnt instead of expelled into the air. What this does is create a situation where in the event of a wreck or rollover, if the breather tube fills with oil this oil can be coughed up into the intake as well.

I set mine up where it comes out of the front of the stator cover and forms a loop in between the frame rails in front of the motor, zip ties in place with the end of it pointing to the ground so anything coughed up can just drip to the dirt. Its out of sight and out of mind. The loop helps prevent water from going into the crankcase if you get into some water crossings.