USB Cable
I have never heard of connecting an MBA (or any other Mac/PC) to a TC in this method. Aside from the fact that it wouldn't work, I'm not sure that such a cable exists. Typically, a wired connection between a Mac/PC and a router is made via ethernet cable. I've never owned a MBA, but I suspect that they are lacking a ethernet port. In that case, you are stuck with a wireless connection unless you purchase one of these (along with an ethernet cable).
Apple USB Ethernet Adapter - Apple Store (U.S.)