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The metal line to the automatic choke goes to the exhause manifold. Its probably just rusted in two. Most are. The lines going into your firewall, one is supposed to be for the manually operated windshiled washer pump, and I'm not really sure aobut the other one. Take a further out picture.
Ill have to take a pic later when I get home. They are very soft lines. Ones about the length to the radiator bracket while the other is only halfway down the fender.
I can't tell by your picture exactly what you are referring to. If it is a soft rubber line, it could be your windshield washer hose going from the bag to the cowl.