I would say the answer lies within.
For me it would depend on the dog, it is in pain? Is it eating and drinking, using the bathroom? If there is no pain, and everything else is fine, then why put it down?
It may be old and slow, but is it happy to see you? Does it wag it's tail?
Putting a dog down, especially if it is a family member can be one of the hardest things you would have to do. I would seriously weigh my options before doing so. If it's just old, but everything else is functioning normally albeit a little slower, then why put it down?