I was examining my 1988 f150 5.0 engine and I found a broken hose thats pretty small in diameter. The broken end was near the battery tray and the other end went under the intake manifold and I bielieve it conected to the back of the throttle body.

 

Hard to tell but it looks like the vacuum line for the charcoal canister. It pulls in excess fumes from the gas tank(s) to be burned in the combustion chamber.

Edit: the charcoal canister is below the battery tray mounted on the inner fender, or at least it was on my '90 5.0.

 

I think your right. My charcoal canister only has one vacuum line connected to it and the one that goes to the throttle body is disconnected to it. I tried to see if the vacuum line fit on the charcoal canister, but the line seemed to be too small

 

Purge line would be my guess too. Look for a "purge valve" inline near the throttle body.
Some of the hoses to the charcoal canister are weird shapes that go from one size to another. You may have to shop the wrecking yard or get creative.
You'll want to fix it though, cause when your purge valve opens you'll be sucking air.
And without the purge valve, the fumes build up, the canister gets overloaded, and the truck has kind of a gassy smell.

 

iphone went to wrong thread.