Difficult to start and stalls at red light and stop signs.

[monti0007]

Everything was fine a few weeks after i got my 2002 gz250 in march 2014. Its july now and my bike is giving me a hard time starting (i have to use the choke and try maybe a dozen times) and also idling while at a stop sign or red light. Multiple times Ive had to restart it at a red light. It doesn't go faster than 40 unless I get wind drift or Im going down a small hill. I changed the oil, battery, and put new gas in, and currently have the carburetor out and getting cleaned for tomorrow. I noticed on the right hand side of the carburetor there is a black tube coming out that leads into nothing. I was thinking this might be it. It comes out from the right side, but on the backer area.