The average Fairfax homeowner will pay about $216 more in property taxes during the next fiscal year, after the county Board of Supervisors on Tuesday approved a one-cent increase in the residential tax rate as part of its overall budget process.

The county had initially advertised a two-cent increase, from $1.075 per $100 of assessed value, to $1.095. Instead, supervisors made some cuts, including freezing county employees’ pay in most cases, eliminating 41 jobs and reducing the amount sought by Fairfax County Public Schools. The final rate for fiscal 2014 will be $1.085 per $100 of assessed value.

Board Chairwoman Sharon Bulova (D) said she had hoped the new budget wouldn’t be so tight. Spending is increasing 1.37 percent.

“Sadly, the optimism was short-lived,” Bulova said. “This year our country has incorporated new language into our common vocabulary — congressional inaction, fiscal cliff, sequestration— policies and situations that have thwarted those hopeful early signs of recovery.”

Supervisor Pat Herrity (R-Springfield) said the penny increase was still too much, and he was the only dissenter in the 9-1 vote approving the new rate. Herrity said that with property assessments rising, the increased tax rate translates into a 4.5 percent increase on taxpayers, and that it will be much worse for condominium and townhouse owners who saw their assessments rise by as much as 20 percent.

“We as a board spend a lot of time talking about helping people in need,” Herrity said. “I can only say that when it came time to tax them, they were sadly forgotten.”

Spending for Fairfax schools accounts for more than 50 percent of the county’s $3.6 billion general fund expenditures, and the school district had sought a 5.7 percent increase over last year. Supervisors knocked that down to a two-percent increase, allocating $1.89 billion to the school system. The board also approved, by unanimous vote, some “guidance” language to the school board urging the school system to establish a permanent, independent auditor, because a similar auditor for the Board of Supervisors has saved the county millions in money and efficiency.

The $216 tax increase is based on an estimated average assessment of $465,713, a 3.5 percent increase over last year’s mean assessments. Fairfax housing values are slowly rebounding after plummeting from an average value of more than $542,000 in 2008 to about $433,000 in 2011.

Supervisors also eliminated a projected budget shortfall of $169 million during their budget markup. The budget is set to be formally approved on April 30.

Supervisor Michael Frey (R-Sully) said he didn’t think the board had done enough. “To me, this is nothing but treading water and putting off decisions on removing money from reserve funds we’re going to need down the road.”

Supervisor Penny Gross (D-Mason) responded, “I would rather tread water and swim with the rip tide than drown.”