By camera & detector I've had a broken line under the slab located. Since there is a break here, how likely is it that the whole line is at the point of needing replacement? Is rerouting the line around the house a viable option?

What kind of line is broken, sewer drain, hot water, supply? Rerouting might be an option in warm climate areas. However, you eventually need to reconnect to the existing system and that requires breaking concrete. Might as well break the concrete at the point of the break. The break is likely caused by settling rather than old age and deterioration. Slabs can easily crack over time especially if you have a high water table or sandy soil. You'll know when you get to the break.

"how likely is it that the whole line is at the point of needing replacement? Is rerouting the line around the house a viable option?"

When we have that problem we open up the slab, drain the house down and repair the leak. Rerouting's not a option. This might be a main instead of a branch that has a leak and you'll end up repiping all the branches that came off it. Good luck, Tom