There is enough equity in my mortgage to cover my line of credit - when is it a good idea to pay off my credit by increasing my mortgage?
There two answers, either never or now; which one is correct for you really depends on how you view the debt, and your discipline of paying it off.
As mentioned by @Vitalik, your absolute cheapest alternative may well be to keep the debt in your line of credit and merely pay it off. The fact that it is a higher interest rate than your mortgage may help to focus your pay-back to as short a time as possible.
If you pay back the debt over say a year, the overall paid interest may well be lower than if you had instead increased your mortgage. You could do a simple interest-rate calculation to determine if this is the case, using the difference between your credit-line rate and your mortgage rate. (Also to take into account, is any tax implications - I understand that in the USA mortgage payments are somehow tax deductable?)
If on the other hand, you do not plan to pay back the debt quickly, then you are certainly better off getting it moved to the lower-rate mortgage right away.
Do be aware of a subtle trap, however: you may lull yourself into a false sense of security as to the absolute amount of money you can borrow and owe. If you were to again run up your credit line, because it is available, you may find yourself in a worse situation than you meant to.
Doing this kind of credit-line to mortgage probably makes sense for durable assets, like a house addition or renovation, but I would personally recommend against it for even something like a car purchase, as you can end up paying more over time.
if you are not planning to pay it off any time soon you might as well do it now. Mortgage is probably a low fixed rate. Refinance does cost money and getting a new 30 year mortgage may look attractive in a short term but will definitely cost you a lot in the long run.
I wouldn't do it but rather try to pay it off as soon as possible.
Part of the answer depends on the various interest rates, fees and balances involved. For instance, refinancing often involves up front fees which mean that it isn't worth it even if you can get a lower rate by doing so. Exactly where the cutoff point is depends on your specific situation.
Perhaps more importantly, though, is what the line of credit was used for. Remember, by placing it on the mortgage, you are guaranteeing this debt with your house. Would you want the bank to foreclose on your house because of this debt?
Securing debt with your house makes sense for certain debts, such as purchasing the house itself, performing renovations, landscaping and home improvements, and purchasing major appliances which are reasonably considered part of your home. For other large purchases (vacations, cars, miscellaneous credit cards) you should carefully consider the pros of a lower interest rate against the con of placing an additional lien on your home.