What hose did I just tear off my rear axle?

I just noticed that I have a torn hose that comes from a nipple on the drivers side of the rear axle to a hose that tucks in in front of the gas tank. Close up is of the nipple with remnants of hose and the further back shot shows the general area and the hose hanging down that tore free.





I’m going to take this in to get it repaired but I’m not sure it’s safe or advisable to drive it to the shop this way. Is that hose for the brakes or the diff or what?

https://www.bing.com/videos/search?q=Ford+F150+differential+vent+hose+1986&docid=608009164287641548&mid=297A51BFC0FC9B2AE521297A51BFC0FC9B2AE521&view=detail&FORM=VIRE

That's the vent to the rear axle.  The hose gets hard and breaks.  Get a new hose and run it up to where that one stops.  There should be a clip and a little "button" that keeps varmints out.  Re-use them.