Here are the requirements for you to claim your grandmother as a dependent:

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.

2. The person either (a) must be related to you or (b) must live with you all year as a member of your household. 

3. The person's gross  taxable income for the year must be less than $4,150 in 2018. Social Security Benefits should not be included in this income limit.

4. You must provide more than half of the person's total support for the year. Social Security Benefits must be included in calculating whether you provide more than half her support or not. The worksheet on p. 16 of this IRS Pub. can help you determine whether you provided more than half her support or not: https://www.irs.gov/pub/irs-pdf/p501.pdf Paying most of the utilities would probably not be half her support.

5. The person must be a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico.