If I took out a line of credit secured by other holdings, and used that line of credit to pay for part of my house, can I deduct the interest paid on that line of credit?

Unfortunately, these conditions must be met for personal interest to be deductible:

• The loan is secured by your main home or a second home. "Secured" means the home is put up as collateral to protect the lender.
• The home with the secured loan must have sleeping, cooking, and toilet facilities.
• You or someone on your tax return must have signed or co-signed the loan.

The only other deductible non-business interest is investment interest and this doesn't seem to be the case here.  If you borrow money to finance investments, the interest you pay is considered investment interest. Examples include margin interest your broker charges you on loans to buy stocks, and interest you pay on money you borrowed to buy raw land for speculation. If you have investment interest expense, you can deduct it up to the amount of your net investment income.

If you borrow for business or personal purposes as well as investment, you can deduct only the interest expense on the part borrowed for investment purposes.