A home equity line of credit does not affect aid eligibility because the loan proceeds don't count as an asset until it is used, and then it is presumably used to pay bills immediately, so there is no cash in a bank account.

A home equity loan, on the other hand, results in cash in a bank account which must be reported as an asset on the Free Application for Federal Student Aid (FAFSA) if you file the FAFSA after receiving the proceeds of the loan. While one usually reports the value of assets net of any loans secured by the assets (e.g., the value of your brokerage account is net of any margin loans against the account), a home equity loan or line of credit is secured by the home, and the principal place of residence is not reported as an asset on the FAFSA so there's no reported asset value to offset.

I recommend relying on federal education loans before resorting to home equity loans and lines of credit. For example, the interest rate on the PLUS loan is a fixed rate that is usually lower than the interest rate on a home equity loan. While home equity lines of credit currently have lower interest rates for borrowers with excellent credit, those rates are usually variable rates and so are likely to increase significantly over the next few years. Also, up to $2,500 in education loan interest is deductible as an above-the-line exclusion from income (so you don't need to itemize to make this deduction), so the argument that home mortgage interest is deductible is no longer a strong argument in favor of HELOCs and home equity loans.