The Fairfax County Board of Supervisors yesterday gave preliminary approval to a proposal that would legalize the rental of rooms and basement apartments in single-family homes. Final approval is expected next month.

The 7-to-2 decision caps almost three years of discussion of the proposal. Final approval would make Fairfax the first area jurisdiction to give its official blessing to so-called "granny flats." Proponents of the measure have promoted it as a means of providing affordable housing for the elderly and handicapped while offering some income to older homeowners who otherwise might not be able to afford rising property tax bills.

Under the proposal, Fairfax homeowners could rent "accessory units" within their homes or garages to elderly or handicapped people as long as the units do not change the exterior appearance of their homes. Homeowners seeking to qualify under the measure would be required to send notice of their plans to all property owners within 400 feet of their property, and would also be required to undergo county review every four years.

Providence District Supervisor James M. Scott called the measure a "very, very small step" toward offering assistance to elderly and handicapped citizens who have sought to rent out portions of their homes for income, companionship, or the security that a tenant could bring. He said tough restrictions incorporated in the measure would limit to about 10 or 15 the number of homeowners who can take advantage of the concept in its first year.

A loose coalition of homeowners had opposed the measure, arguing that a change in the zoning laws could alter neighborhoods and decrease the values of homes.