Lease
A lease is a contract that gives a tenant the right to live in a property for a set period, commonly twelve months, in exchange for rent. It fixes the rent, the term and the duties of both sides, and every adult named on it is responsible for the full amount.
The 3x rent rule is applied before the lease is signed, using the rent that will be written into it. If the rent is $1,500, the applicants on the lease need $4,500 a month in gross income between them.
Who signs matters for the math. Income from anyone who is not on the lease is not counted, and everyone who is on it can be pursued for unpaid rent. At renewal, a landlord can re-check income against a higher rent, though many do not for tenants who have paid on time.