Brooke Amendment
The Brooke Amendment is a 1969 change to federal housing law, sponsored by Senator Edward Brooke, that capped rent in public housing at 25% of a tenant's income. Congress raised the cap to 30% in 1981, which is where the 30% affordability rule comes from.
The amendment applied only to public housing, but its ratio spread. The 30% figure became the general yardstick for whether any household can afford its housing, and it still defines a cost burden in federal statistics.
Private landlords settled on a neighboring number. Requiring 3 times the rent holds rent to 33.3% of gross income, a slightly looser test than 30%. New York City's 40x rule matches the 30% figure exactly. The 30% rule guide compares them.