Just adding my thought, true Line-out terminals give fixed sound signal output, irrespective of the Volume/Tone control levels. So when a woofer is connected to it, it will be at its full volume, not matching with the Volume level of the box. Or there should be a volume control on the woofer and every time it has to be balanced with the Volume level of the boombox.
The subwoofer out of Amps are variable, in proportion to the overall volume & tone controls levels.