There are multiple effects here:
- It should lower your utilization, as it will give you a higher overall credit limit but not change the amount that you owe. This helps your credit rating.
- Applying (which you may have already done) can lower your credit in the near term, as the credit inquiry hurts your credit rating. This effect fades pretty soon and will be gone in six months to a year.
- If you just use your now open credit cards to borrow more, that will hurt your credit rating.
So if you're ready to work on your debt, this can work as a first step. Just remember, the thing to do is stop borrowing. So pay off your credit cards and then throw them away. They're lousy, high interest cards; you don't need them. You can keep two to four cards that are as cheap or cheaper than your line of credit. Eventually pay them off every month.
Assuming that this makes the line of credit the highest rate debt, pay that off next. Pay as much as you have left each month after paying the minimum on lower rate loans.
The key is to consume within your budget. If you don't do that, then nothing else will matter. Your credit rating will get worse because your debt gets worse.