Thanks everyone! Ya, we were pretty certain that it's priority to pay. We were just wondering about how much it'll do to our credit score and if there's an option to pay it down to 1k or something and then make tiny payments monthly so we can keep the line of credit open and average age of accounts up.
What's your credit score now? Do you need a line of credit in the near (e.g. 6 month) future?
What the credit agencies want to see is at least
one line of credit open for >2 years, preferably 5 years, and a history of having paid on time in the last 7 years (even on accounts that are now closed). They don't care about the average age of debts much, if at all. If you've had a credit card for several years not much will happen to your credit score should you pay off your SL. In general, it's a good idea to keep your longest credit card open regardless (I made the mistake of allowing mine to close).
Even still, on-time payment and your available credit ratio are two of the biggest factors. When I applied for a mortgage I had allowed all but my most recent cc to close (which was just 1y, 11mo) and I still had a score of 760, qualifying me for the best rate. Even though SLs won't show up on your active credit, they ARE still listed on your full credit report, as are other credit cards you may have had in the last 7 years.