How to set up a ethernet cable connection to a MacBook Air?

With the ethernet cable plugged in, and the networks screen is displayed on my MacBook Air, there is no display of an Ethernet Cable on the left side of the networks screen. The ethernet cable isn’t working. Why does the answer I got say that once in the networks screen, on the left, ethernet cable will be displayed when it isn’t, yet it is connected properly?

I purchased a MacBook Air 9 months ago for my daughter. She studies in her bedroom but the wifi signal is too weak. I bought a long ethernet cable and plugged it into her Mac with an adapter and the other end into our router. Went to settings-preferences-network. There is no display for the ethernet cable on the left as Apple informed us there would be so we could configure the ethernet cable connection. WHY?

Ethernet cable is not displayed in settings-preferences-networks though the ethernet cable is plugged in the Router. This answer is wrong. It’s a 9 month old MacBook Air. How do we use an ethernet cable connection. The ethernet cable is plugged with the adapter. Could the adapter be faulty?