The bank increased the rate on my variable home equity line of credit (HELOC) without providing any notice. Can it do this?

Yes. The term "variable" refers to the interest rate. It means that the interest rate on your home equity line of credit (HELOC) is tied to an index or formula that reprices periodically. At the time you contracted for the loan, the bank was required to provide you with a disclosure that explained this variable rate feature.

Since the variable rate feature was disclosed at the inception of the loan, the rate change is not considered a change in terms. Therefore, the bank doesn't have to notify you at least 15 days in advance.