Graham was born and raised in Washington County, Kentucky. He studied English and became a schoolteacher, moving to Hancock County, Illinois, in 1836 to teach. He returned to Washington County, Kentucky, and in 1839 or 1840 ran an unsuccessful campaign for state representative in the Kentucky General Assembly.
Graham was born and raised in Washington County, Kentucky, where he studied English and became an educator. He then moved to Hancock County, Illinois, in 1836 to teach, before returning to Washington County, Kentucky, and running for state representative in the Kentucky General Assembly in 1839 or 1840.