Where do this hose to be supported to be hooked to?

 

Axle breather. Should clip up by the spare tire somewhere. Just zip tie the end up high. Some folks extend the hose to the cavity behind one of the taillights to keep it as high as possible and keep it from getting water into it.

 

It's a rear axle vent line. As the axle increases in temperature, the air pressure inside the axle likewise increases. To accommodate the increase in air pressure resulting from this heat, manufacturers add a vent tube to the top of the axle as means of releasing this pressurized air to the atmosphere. Just a generic pic I Googled:

 

Thank you for the replies. I’ll tie it up when I’m home

 

Wow! Costco tire crew hooked it up for me. Awesome!