If I invest money from my home equity line-of-credit by loaning it as a mortgage lender for an LLC to purchase and improve a house (with this money) and they sell the house and pay me 15% (plus my initial investment), what kind of income is that to me and what is the tax rate on it?

Check with the mortgage lender who they are reporting your income. If they give you 1099-misc, it will show how much you earned.
1099-misc (nonemployee compensation) income: You are self employed or independent contractor. You must file your tax return if yourself employed income is $400 or more. You will report your income and business related expenses on schedule C or C-EZ (Form 1040). Then you put net income (or loss) on line 12 of Form 1040. This income is subject to SE tax at 15.3% (this is shown on line 57 of Form 1040). For this you will use schedule SE (Form 1040). For 2012 after payroll tax cut the SE tax is 13.3%. Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor (http://taxipay.blogspot.com/2008/04/tax-filing-by-self-employed-sole.html)

MukatA covers it we.