When you sign up for a broadband service your existing phone line is split into two, like virtual 'pipes', one inside the other if you like.
The outer, larger, pipe handles high-speed digital data and sends it from the Internet to your computer and vice-versa.
The inner, smaller, pipe remains as an analogue conduit and handles speech traffic in the normal way. You can make calls or send and receive faxes on the line at the same time as digital data is flowing in the outer pipe. At the exchange end there is some hardware that separates the two data streams and sends them on their way - voice goes into the BT telecoms system and digital data goes out to the Internet via your ISP.
The broadband service effectively makes two lines out of one. You still have the same telephone number for the analogue line, but the ADSL connection doesn't have a number - it can't dial anything anyway. When you connect to the BT exchange ADSL equipment your modem doesn't dial anything, it handshakes with an exchange gateway and authenticates you via your ISP.
You can't connect a fax machine to the ADSL side of your line - it wouldn't work. In any case the plug connector for ADSL is different to the one on the fax - take a look at your microfilter.
This is the first part of the Word help on sending faxes, you note it talks about a 'fax provider'. Do one of the following: In Microsoft Office Word 2003, Microsoft Office Excel 2003, Microsoft Office PowerPoint 2003, or Microsoft Office Document Imaging (MODI), on the File menu, point to Send To, and then click Recipient using Internet Fax Service. From Microsoft Office Outlook 2003, on the File menu, point to New, and then click Fax. The first time you use fax services, you will be prompted to sign up with a provider. Click OK to open your Web browser, and then follow the signup instructions on the Web site. Close your Web browser, and then return to the Microsoft Office program you want to fax from. Repeat step 1. An e-mail message will open in Outlook with your document attached as a .TIF (image) file, or you can attach a file to the message.