The federal minimum wage is presently $7.25. The states in this grey and white fix the state minimum to the federal minimum (map source). The $7.25 was established in 2009. Wikipedia offers some interesting analyses related to the positive and negatives estimated to result from raising the minimum to $15.
In 2021, the Congressional Budget Office released a report which estimated that incrementally raising the federal minimum wage to $15 an hour by 2025 would benefit 17 million workers, but would also reduce employment by 1.4 million people. It would also lift 0.9 million people out of poverty, possibly raise wages for an additional 10 million workers, and increase the federal budget deficit by $54 billion over ten years by increasing the cost of goods and services paid for by the federal government.
Based on a 40 hour week and say a 50 week year, the $7.25 wage would generate an income of $14,500. The poverty level according to the federal definition appears in the following table.
Various federal assistance programs use these values to determine eligibility and are based on 130-150% of these values (see the link above).
One way to think about this is that businesses that pay the minimum wage are usually relying on taxpayers to subsidize the basic living expenses of their employees. For example, the Affordable Care act provides some subsidy to those making less than 400% of the poverty wage.
Any adult familiar with the cost of food, housing, transportation, medical care, child care, etc. should understand how limited an income of $14,500 a year really is. As a reality check, the following data represent state-by-state estimates of child care costs. Roughly half of the states require more funds to pay for the care of one child than an adult would make at the minimum federal income.