[Joe Sr.]

I would give it no more than a week personally

I've got yeast I've been re-using for over a year.  Treat it well, be sanitary, build it up in a starter and it will last much longer than a week.

Drinking a tripel brewed with yeast that was first pitched about a year and a half ago or so.

Was it from a half used slant that sat in the fridge a year and a half then just pitch as is?

Nope.  Slurry collected from a previous batch.  Half a vial would be enough to build up in a starter.  I certainly wouldn't pitch it as is.

I grew up a six month old ESB slurry about a month ago and pitched it into a stout.  It rocked along and the beer tastes great.  I may actually be seeing greater attenuation in the later generations, but for me that's just fine as I'm starting with some pretty high OGs and don't want the beer too sweet.

[klickitat jim]

Ya my short answer to the half used slant being ok for a week was as-is. It probably would need some TLC to be good for a year and a half.