Thanks to all who responded with useful information. After I got home,
I turned off the feed to the hot water tank, and as you all suspected,
the meter stopped turning and the noise stopped. So, the problem is as
you all stated- a broken pipe in the slab. Also, I compared our water
usage, and it is twice what it should be since the last reading, 30
days ago.

The insurance company has been called, and the adjuster will be here
shortly.

I have a friend who lives in a different devlopment and had similar
work done He liked the people he used- they were fast, and not the most
expensive (or cheapest), so I may use them, but I have a few questions:

What is the "right" way to fix this? Find the leak and fix that one
section of pipe? Replace the entire line? What about it breaking
again? Any way to prevent it? How come I don't have any
visible/detectable water damage?

An alternate routing through the ceiling may be possible, but could be
more expensive, as all the rooms the line would need to run through are
completely finished, and I don't think it's a straight run- I'll ask
the adjuster what he thinks.

Thanks again.