The Fairfax County Board of Supervisors appeared headed yesterday toward cutting the county's real estate tax rate by about 10 cents.

The board delayed taking any action on reducing the current tax rate of $1.74 for each $100 of assessed value on a home until it finished house-long deliberations on the county's $586 million budget proposed for the fiscal year that begins this July.

"It appears that all of us are taking about cutting the rate by around 10 cents," said board member Audrey Moore (D-Annandale).

A 10-cent cut in the tax rate - a reduction of almost 6 percent - still would result in higher average property tax bills because property assessments rose an average of 8.7 percent countywide last year.

Assessments on single-family homes generally rise faster than other types of properties in the county, including commercial establishments and developed land and assessments on most. Fairfax homes rose more than 8 percent last year.

Under a $1.64 rate, the owner of a typical $69,000 house who paid $1.200 in taxes last year would pay $1,246 this year as a result of the rising assessments. Under the $1.74 rate, he would have paid $1,322.

County Financial Director James McDonald told the board it would have to cut $8.3 million from programs already included in the proposed budget to offset to 10-cent tax rate itself in "a poor financial posture" in the next few years if the board balanced the tax cut by using $13 million from an emergency public works fund, cash balances from the current fiscal year and reductions in the proposed $320 million school budget.

"It's not likely we'll have the same cash balances in the future that we have now," McDonald said earlier.

The board cut the real estate tax rate in 1975, an election year, and was forced to raise it again the following year, when anticipated revenues did not materialize.

The $568 million budget, which County executive Leonard Whorton has termed "conservative," represents a 15 percent increase over last year. The proposed $343 million general fund, which pays for the day-to-day costs of running traditional county programs, has increased 11 percent over last year.

Whorton said most of the increases in the general fund, financed almost entirely by county tax revenues is due to the inflation and rapid county growth.

The budget calls for no new major programs and services, but does include money for three new fire stations, 98 more firemen and policemen and 91 other jobs scattered throughout county agencies. The manager said all are needed to meet the demands of growth.

These additions would cost $2.4 million. The country government share of the proposed school budget - $167.5 million - accounts for nearly half of the general fund. The remainder would go for a variety of government functions including general government ($37.2 million). social and health services ($28.5 million), justice ($2.5 million) and public safety ($34.7 million).

In other action, the board attempted to head off a threatened cut in federal money for the county by sending a letter to the U.S. Department of Housing and Urban Development explaining county policy on public housing.

Two weeks ago, HUD said it will withhold $3.8 million in federal grant money, which in the past has paid for storm drainage systems, road improvements and home loans, unless the board could justify its decision to impose a 90-day delay on construction of Rolling Road Estates, a 100-unit development in the Springfield area for low-and moderate-income families.

The board also decided unanimously to refuse to participate in funding any rail lines in the Metro transit system unless rail lines in Fairfax are included in the system as originally planned.

The board's resolution comes as the federal government and Washington area local governments are looking for ways to fund construction of the originally planned, 100-mile rail system. Proposals to reduce the size of the rail network have been resisted by all local governments.

The board expressed concern that the Fairfax line planned for Franconia might not be built as proposed if the Metro system is shortened, a possinility discussed by the Metro Policy Steering Committee last week.