BleepingComputer.com: How my ISP knows it's me and my router

I'm quite familiar with communications but one question I cannot find an answer for is how my ISP knows that it is me connecting via DSL down my phone line (prior to using my computer). As far as I can tell, that must be done solely by my modem/router being physically connected to a particular phone line.

The router has no outgoing password that I'm aware of. Even if that were the case, or something like the MAC address of the router were used, it would mean you could only use the ISP's modem/router. Anybody?

So, I do not have DSL but rather Broadband - each time I switch out my router, I have to call my ISP and provide them with model number, serial number, and MAC for the router - I would think a combination of these would provide the ISP the needed info to make sure it is you. And some ISPs will provide you with a router/modem that can only be used for connection - just depends on the type of account and company.

Thanks. I've never bothered to read my agreement to see if you can change modem. It was one of those temporary one page agreement of services on sale that became permanent! What you say makes sense and prevents anyone connecting at the local JB and pretending to be you, or at least using your bandwidth. It's strange that I cannot find any information by searching the Internet. Tons of articles on security, but not this.