Faulty battery, bad alternator, or both (photos)

The alternator belt is tight.
I was thinking the same thing, the reading at the battery with the car on should read higher, not lower.

Unfortunately, at the moment I don't have anything other than a way to test volts.

It may be worth a trip up to the store to have them test it.

Edit: I should also mention that I'm getting increasingly slow starts. Not sure if that helps with diagnosis...

Is there any way to tell if this the original 40yr old alternator?