I’m over 75, retired/on SSI, with an earned income of $17,400, living in RI. Turbo Tax is showing I owe Federal taxes of $79. My income is not taxable; what am I missing?

We need some clarification.    When you use the term "SSI" do you mean Social Security benefits that were on a SSA1099?   Or do you mean Supplemental Security Income?   Social Security and SSI are not the same thing.   

Did you receive Social Security and earn an additional amount of $17,400?    Or is that the amount of Social Security you received?   

If you have $17,400 of earned income, that is taxable unless you're Married Filing Jointly.

In addition, Social security (including SSDI) becomes taxable when your income, including 1/2 your social security, reaches:

Married Filing Jointly(MFJ): $32,000

Single or head of household: $25,000

Married Filing Separately and lived with your spouse at any time during the tax year: $0

What kind of income?  Did you get a W2 for it or some kind of 1099?  Why do you think your income is not taxable?