The Fairfax County Board of Supervisors cut the real estate tax rate by a dime yesterday in adopting an election year budget that stresses economies and gives teachers and other government workers smaller raises than they have demanded.

Nevertheless, because of rising property values, the average homowner's tax bill still will go up by about $16.

Last year the owner of a house valued at $68,200-the county average in 1978-paid $1,118 in real estate tax. This yearthe value of the average home has increased by 8 percent, to $73,656. Even though the tax rate is cut from $1.64 to $1.54 per $100 of assessed valuation, the home's owner can expect a tax bill for $1,134.

The supervisors spent six hours yesterday reaching agreement on the cuts that brought the budget total for the fiscal year that starts July 1 to $624.1 million and permitted the cut in the tax rate.

The most controversial feature of the budget is its provision of 5.15 percent raises for all 20,500 county employes, including school teachers.

Workers' groups have called this inadequate, and the Fairfax educations Association (FEA), representing the teachers, has threatened a "work-to-the-rule" job action that would slow down some school work and cut slow down some school work and cut back on supervision of extracurricular activities.

The FEA has scheduled a protest rally for 6 a.m. today at the Elks Lodge, 8421 Arlington Blvd.

The teachers have sought 9 percent raises, which they say they need in affluent Fairfax County where the median family income is $28,500. The average county teacher is paid $18,500 a year.

Over the objectionso of many county employes, the supervisors voted earlier this month to raise board members' salaries by 23 percent on Jan. 1 when a newly elected board is sworn in. The supervisors, who now make $15,500 a year, have defended the move by pointing out that their salaries have not been raised in four years.

The major victim of the budget cutting was the county school system, which lost $1.4 million of the $180.9 million it has requested of the county. The superviors promised to give the schools another $400,000 if it loses the federal impact aid that U.S. government gives to localities to compensate them for teaching the children of federal workers.

Congress has proposed cuts in impact aid of up to $6.2 million for Fairfax schools. County officials said they believe that the funds, which Congress has threatened to cut off in past years, actually will be denied this year.

The budget calls for few personnel cuts, and the spending program was described by Action County Executive J. Hamilton Lambert as one that keeps "increases to the minimum amount necessary" to continue "the current high level of service" the government provides.

The budget total of $624.1 million is down 9.9 percent from the current year's $680 million budget, although the county's contibution from its tax revenues-$374.7 millcon-is up 8.5 percent. The rest of the budget is financed by state and federal funds, bond sales, fees and other sources.

During yesterday's budget session, the supervisors approved several spending increases, including a $350,000 subsidy for the Reston commuter bus system. The sum is enough to keep the Reston buses bunning for about six months.

The board also authorized $75,000 for new bus service to the Great Falls area. The buses will run twice each morning and afternoon between Great Falls and the Pentagon.

The board approved 25 new positions for the police department, 57 for fire and rescue, 11 for social services and 17 for the courthouse and jail.

The most dramatic increase in the budget is a 50 percent jump in funds the county must pay as its share of the Metro transit system. The amount rose to $12.1 million from the $8 million in the current fiscal year budget. The increase relfects a new cost-sharing formula that falls more heavily on the county.

At the request of Juvenile and Domestic Relations Court Judge Philip N. Brophy, the board also approved $71,022 to fund 12 group homes for "difficult" children in the county's juvenile court system. The group homes have beeb a political liability for the supervisors because of complaints from constituents living near the homes.

Funding for the schools, which at $179.5 million represents the largest item in the county's operating budget, was up about 11 percent more than the current year because of a decrease in state and federal funding for schools.

Money granted the school system may be increased, the supervisors said yesterday, if fuel costs in the coming year increase dramatically, as they are expected to do.