The Fairfax County Board Supervisors rejected a proposal yesterday to raise the property tax rate and gave preliminary approval to a budget 15 percent larger than this year's spending program.

The $442.1 million budget tentatively approved will give county employees, including teachers, 8.5 percent raises. The supervisors avoided raising taxes by deciding to cut $4.4 million from Acting County Executive J. Hamilton Lambert's budget proposal.

The largest cut is a $2 million reduction in the county's $19.1 million contribution Metro officials have requested for the Washington area bus and rail transit system. That cut is likely to cause a reduction of up to 25 percent in weekday county bus service plus an increase in bus fares, according to county officials.

Despite the decision to reject Lambert's call for a 4-cent increase in the property tax rate of $1.54 per $100 of assessed valuation, homeowners can, expect their tax bills to increase because of inflation.

Higher assessments will add about $140 to the $1,061 tax bill for a home valued last year at $69,060 -- the median value of homes in the county.

Board Chairman John F. Herrity (R) claimed that the $4.4 million in budget cuts indicate a county move toward the budget-cutting enthusiasm displayed when California voters approved their Proposition 13 taxing limitation two years ago.

Other board members disagreed, saying the $4.4 million in cuts were relatively small.

"These weren't deep cuts," said Supervisor Joseph Alexander (D-Lee). He said members of the county school board indicated privately they can absorb the proposed $1.24 million cut in school spending "without too much problem."

Gerry Gripper, president of the Fairfax Education Association, which fought vigorously for the 8.5 percent raises for almost a year, was cautious in offering praise for the board's preliminary decision. The association, which represents most of the county's teachers, has been calling attention to last year's more than 13 percent inflation rate and the close to 20 percent annualized rate for 1980.

"I could have been much worse," said Gripper, noting that the raise still needs final approval from the supervisors and the school board. "The county got off cheap, to be honest," he said. "We could have made a good case for a higher increase."

The new budget contains no major new programs, inflation accounting for most of the 15 percent increase in costs. Most of the amount will fund big increases in spending for schools and energy, with some interest also in spending for police and fire protection.

The reduction in weekday bus service to the county would occur on so-called marginal routes where ridership is low.

Metro spokesman Cody Pfanstiehl noted that Metro suggested such a cutback "a long time ago . . . We're glad they want to do it."

The supervisors decided earlier this month to impose cost controls on the bus and rail system. Officials in Arlington and Alexandria also have voted recently to fund Metro at levels below those requested.

Some supervisors apoligized at cutting the county's $217.4 million share of the school budget by $1.24 million. But M.E. Cale, a budget specialist for the school administration, said the cut, which amounted to less than half of one percent of the school budget request, was "very responsible and very spare in light of the fiscal conditions of the county and the nation."

School officials were said to be angry at a decision by the supervisors to use investment earnings from county construction funds to offset expected losses in federal assistance to the county.

Under the plan, which received unanimous approval, interest on bond funds previously set aside for county construction projects will be returned directly to the operating budget for disposition by the supervisors. Such investment revenues currently are applied toward construction costs.

County School Superintendent Linton Deck had criticized the plan, saying it could leave school construction projects high and dry if inflation unexpectedly boosted costs. Acting Ececutive Lambert said yesterday it is extremely unlikely that the supervisors would deny further funding in such circumstances.

The supervisors told Lambert to make more than a million dollars in cuts in his proposals for county government spending but did not specify where they should come.