Fairfax County’s Board of Supervisors voted along party lines Tuesday to give formal approval to a $6.1 billion budget that reduces the property tax rate slightly, but raises the effective tax on homeowners, along with several fees.

The Board of Supervisors’ adopted budget, which reflects better-than-anticipated sales tax receipts and slowly improving home values, also scraped together additional school funds to help implement full-day kindergarten throughout the county and adds funding for 39 new employees, such as school nurses and staff to aid the mentally ill.

Although the board voted to reduce the property tax rate to $1.07 per $100 of assessed value, the average homeowner will pay about $22 more a year because of rising home values. Sewer service charges will also go up about 14 percent to $6.01 per 1,000 gallons from $5.27. Regulatory and licensing and permit fees will rise an average of about 3 percent.

The Democratic-led board passed the budget by a vote of 7 to 3, with all three of its Republican members voting no.

Board chairman Sharon S. Bulova (D) characterized the budget as a steady-state plan that balances the need for services and the burden on residents. She said that even after the re-imposition of a car-registration fee last year and higher sewer fees, the average taxpayer is still paying less per year than under the budget that was in place when the current board took office in January 2008.

The adopted fiscal 2011 budget is built around an increase of 1.97 percent in revenues and includes $3.38 billion in spending, or about $69.4 million more than the adopted 2011 fiscal budget.

The budget does not include pay raises for county workers for a third consecutive year, although the board has also directed that any savings or left-over balances from the current fiscal year could be used for compensation increases as early as October.

The board agreed to give the schools $1.77 billion, or about 0.16 percent more than the previous year. It also found almost $3 million in additional savings from the elimination of the after-kindergarten portion of the School-Age Child Care program and other funds that it would like to see used for full-day kindergarten.

The 2012 fiscal year, along with new tax rates and fees, takes effect July 1.