Americans are desperate for relief. The rate cut is a glimmer of hope.

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Subscribe to enjoy similar stories. The Federal Reserve’s interest-rate cut on Wednesday will take time to work its way through the American economy. And not everyone will feel its effects right away.

But for some, the move will amount to a big change—or at least the start of one—and those changes will add up. The varied impacts will stretch from struggling restaurateurs north of Phoenix to Miami homeowners who need to downsize to get by. All told, the amount of extra breathing room in American budgets could shape the economy in the years ahead.

Officials on Wednesday cut their benchmark rate by 0.5 percentage point to start, the first step in lowering what Americans will pay for business and auto loans, as well as credit card balances. Mortgage rates already have been falling for months in anticipation. Now, the question is changing from how quickly higher rates will cool U.S.

growth to how quickly lower rates can support it. The economy is more like an ocean liner than a speedboat: Just as it took time for higher rates to slow things down, it will take time for rate cuts to speed things up. The cuts will make many household budgets stronger, on balance, and potentially begin to lift some of the bad economic vibes that have puzzled Washington and Wall Street.

Across the world’s largest economy, those little differences are multiplied by millions of people who borrow money to finance big purchases, invest in companies or buy day-to-day necessities. Take Alessandro and Clare Segala. The couple early this year made a bet that the typically slow-moving Fed would spring into action.