Sending a Fax without a fax number

If you want to send/receive faxes, then just connect the machine to the phone line. The phone company does not sell/lease "fax" lines or numbers.

WiFi is for networking devices, not phone equipment. If you connect this HP by Wifi, then you could use the printer/scanner as a wireless network printer. Sending/receiving faxes from/to the PC using the HP over the phone line would depend on software installed on the PC and how the HP is configured (e.g. would received faxes be printed (on paper) immediately or sent (softcopy) to the PC?)

Addendum:

I do not use a regular phone line.

I have seen online services that allow this from the PC, is that the only way to do this?

The fax is a phone device/service. If you choose to use the "online service", then the fax capability of the HP is totally irrelevant. The Internet and your PC with the "online service" replace the fax machine at your location.

BTW most businesses have been able to accommodate me when I ask them to exchange e-mail attachments instead of faxes. Scanning the document(s) and then composing the e-mail is more work then sending a fax, but it is doable when your faxing requirements are so infrequent.