Equipment needed- phone only

I have been debating cancelling all other services and keeping phone only. The phone program I have is a measured line, and I really only use the thing for alarm system, and occasionally Dr. Offices and the school system will call and leave me a VM. But generally, i would cancel this phone if I wasn't getting it for $10.00/month. 

Looking at my most recent bill, I don't see an itemized charge charging me for a modem. I do see the modem in the internet section of my bill saying (DOCSIS3.0 modem required) but no itemized charge. 

So my question is, if I were to cancel all but my phone, would Cox suddenly begin chargging me for this modem? Could I just go buy my own? 

I assume they'll have me put a filter on there if I keep it, but if I have to start shelling out 7/10 bucks a month for modem rental, that sort of negates the measured line cost I get. 

TIA.