In short, my opinion is keep the fax line. You can still manage faxes with your linux box...I'm a fan of Hylafax myself...but sharing a line has always been problematic, regardless of how the faxes are managed. For a home user you can justify the trade-offs, but for a business, I think having a dedicated fax line presents a better business image. Nothing *feels* less professional than trying to call a business an having some computer *decide* I was sending a fax and I get the modem squelch in my ear.
Also, many businesses use computers to *send* faxes these days. In my office, for example, I've configured our server as a fax server. Anyone in the office can print to the fax server as a normal printer and the server handles the actual faxing. One side effect of this, though, is that the server queues faxes. After all, think what would happen if two people "printed" to the fax machine at the same time. The server starts one fax and stores the other and waits until the line is free, then sends the next. The end user doesn't know the difference. They don't have to try again later, or keep retrying if a busy signal is encountered, or deal with any of those inconveniences.
Overall I've found this approach to offer many benefits over a traditional fax machine, but one drawback is calling a system where the line is shared. If the user puts in the phone number (406) 555-1234-1 (the 1 triggering the fax, for example) then the server will usually dial the 1 before the line has picked up...and the fax fails to send because the receiving end botched it. OTOH, most dialers support pauses with a comma, so the phone #
(406) 555-1234,1 will *usually* work, but sometimes the pause is not long enough, so the user is stuck trying 1234,,1 or 1234,,,1 and...in some cases...the pause is too long and the technology on the other end decided it was a voice call. Pause is too short or too long, no in between. A real PITA.
So, as I said, for a business, a fax line is really just a cost of doing business, and I recommend all businesses keep a dedicated line if they do any amount of faxing. If you are looking to save some money, that "dedicated" line doesn't even have to be on premises. Look at services like efax for alternatives. Still a dedicated number, but usually cheaper than paying for a line yourself.
HTH,
-Cliff