Final answer:
Medicaid is the program that provides health insurance to low-income individuals and families, based on federal and state eligibility requirements.
Step-by-step explanation:
The federally funded and state-administered program available to low-income individuals and families who meet federal and state eligibility requirements is Medicaid. Created by Congress in 1965, Medicaid is a health insurance program that targets certain categories of low-income people, such as families with children, the elderly, and the disabled. Each state administers its own Medicaid program, thus benefits and eligibility criteria can vary by state, although the federal government provides funding support. Medicaid aims to ensure a basic level of health care coverage and is particularly important for those below or near the poverty line, accounting for significant proportion of the health care provision for low-income mothers with children and the funding of nursing home costs for the elderly poor.