I was given a separate amount of money by my employer (a separate check) to use for moving expenses. This was NOT included in the total wages line on my W2. On what line on my 1040 form should I declare this extra income?

You do not claim it on Form 1040.

You claim it on Form 3903 to offset your moving expenses UNLESS it completely offsets all moving expenses, in which case it is a wash (non-taxable income).