Stereo Cable Wired to Starter Battery

I noticed a while ago that the stereo battery was wired to the starter battery. I knew if I didn't remove the cable and the stereo was left on, it would drain the starter battery. I rewired the cable to the house battery today.
(The yellow cable is the stereo cable and the other two are for battery monitor and echo charge).

Stereo Cable connected to Starter Battery

Stereo Cable now connected to the House Battery.