The Fairfax County Board of Supervisors approved a plan last night designed to save the county's remaining farms by offering special tax breaks to people who own 25 or more acres of rural or forest land.

Under the program, which will take effect June 30, those who own 25 or more acres can ask to be placed in a special agricultural district in which the county would base tax assessments on the use to which the land is put rather than on its fair market value. The land owners would have to agree to forgo developing their property for eight years.

Qualifying owners will be able to reduce their real estate taxes more than 90 percent in some cases. County staff members estimated that Fairfax could lose a maximum of $1.8 million if all 19,436 acres that could qualify for the program are incorporated into it. But a county survey of landowners indicated there was interest in involving only about 4,280 acres in the plan and the tax loss would be only about $745,000.

The program was approved unanimously, despite earlier misgivings by several supervisors. Supervisor Thomas M. Davis (R-Mason) said he has traditionally opposed such programs because they have been a "tax haven for land developers." Davis said he believes the ordinance passed last night has sufficient safeguards to prevent abuse.

Supervisor Martha V. Pennino (D-Centreville), another early skeptic, said she received a substantial amount of mail in support of the program. She also said she was reassured by restrictions placed on development.

If property owners break their promise not to develop their land for eight years, they must pay six years of taxes at the higher rate, interest and a substantial penalty.

Up to now, only parcels of 500 acres or more have qualified for these agricultural tax breaks, and there are only two such agricultural districts in Fairfax. County staff members estimate that about 250 additional tracts would qualify under the new plan, although much of that land is already slated for development.

On another matter, the supervisors gave preliminary endorsement to a plan for building an incinerator near the Lorton landfill that would burn trash to produce steam and electricity.

The board directed the county staff to forward a study by the MITRE Corp. consultants, which recommended the so-called resource recovery facility, to Arlington, Alexandria and the District of Columbia. Fairfax officials hope to get the three jurisdictions to contribute trash and construction funds, but all three have discussed setting up similar facilities of their own.

The board asked the three governments to indicate by September whether they are interested in the project. A MITRE spokesman said Fairfax could proceed without the participation of all three jurisdictions, but that the costs would be higher.

Fairfax officials say the Lorton landfill, the only operating sanitary landfill in Northern Virginia, is expected to be filled in 12 years if no other facility is built. They hope to have the furnace completed by 1988.