Commuter pass question

Hi everyone,

Hoping to get some clarification.
I am looking to get a commuter pass for work with the starting station being Yokohama and the destination being Shinagawa. I know there are a few different JR lines that travel to those stations, but I also go to some of the different Keihin-Tohoku lines during my free-time. I know the Ueno-Tokyo and Yokosuka line are also usable for faster commuting (and I can still use those lines as there are no gate changes), but I am interested in a pass covering the Keihin-Tohoku line stations.

I went to the Commuter Pass ticket machine to get an idea of pricing, and when I input my start and end station as well as a Keihin-Tohoku line station as an in between (Shin-Koyasu, for example), it showed the line as the Tokaido Line.

So I am a bit confused. Would that commuter pass be line specific, or would it just cover any JR station on any JR line between Yokohama and Shinagawa?

Thanks for your time and help!