LOS ANGELES — The average rate on a 30-year mortgage fell slightly this week, a modest relief for home shoppers facing record-high home prices.

The rate fell to 6.89% from 6.95% last week, mortgage buyer Freddie Mac said Thursday. A year ago, it averaged 6.96%.

Borrowing costs on 15-year fixed-rate mortgages, popular with homeowners refinancing their home loans, also fell this week, pulling the average rate down to 6.17% from 6.25% last week. A year ago, it averaged 6.30%, Freddie Mac said.

Mortgage rates are influenced by several factors, including how the bond market reacts to the Federal Reserve’s interest rate policy and the moves in the 10-year Treasury yield, which lenders use as a guide to pricing home loans.

After jumping to a 23-year high of 7.79% in October, the average rate on a 30-year mortgage has mostly hovered around 7% this year - more than double what it was just three years ago.

The elevated mortgage rates, which can add hundreds of dollars a month in costs for borrowers, have put off many home shoppers this year, extending the nation’s housing slump into its third year.