The average homeowner’s tax bill would increase by $346, he told the board. The money would go to affordable housing, police body cameras, early-education programs and drug treatment services.

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The $4.6 billion spending plan would add 177 positions to the 12,000-person county government and would bring back some services that were cut during the nearly decade-long period of austerity that followed the 2008 Great Recession.

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A new 4 percent tax on movie tickets would generate about $3 million that would go toward expanded library hours at 11 locations, scholarships for county parks programs and field maintenance at local schools.

Hill said the budget is structured around nine priority areas that make up a new countywide strategic plan meant to bring a sharper focus to Fairfax’s government: safety and security, health and environment, education, housing, transportation, vulnerable communities, culture and recreation, economic opportunities and government efficiency.

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“Everyone is rowing hard, but are we all rowing in the same direction?” Hill asked the supervisors, after noting that the county currently has at least 1,250 separate spending initiatives.

He proposed $5 million to purchase police body cameras and hire 13 officers trained to use them, and $1.6 million to continue the county’s “Diversion First” program, which is meant to steer offenders with mental illness or addiction toward counseling instead of jail. He also proposed $2.5 million to staff a police station set to open in the southern part of Fairfax in 2022.

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For schools, the budget calls for increasing the county’s portion of funding to $2.2 billion to help expand early-childhood education programs and build more classrooms.

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County workers would receive cost-of-living salary increases of 2 percent, while the minimum wage for Fairfax government employees would increase by 31 cents, to $15.45 per hour.

Fairfax board members were generally pleased with Hill’s proposals, though some expressed worry about the higher tax rate.

Board Chairman Jeff C. McKay (D) said he hoped legislation making its way through the General Assembly that would grant localities more taxing authority would help the board ease the burden on residents. Fairfax voters rejected a tax on restaurant meals in 2016. But a state law granting such authority would allow the board to simply pass such a measure.

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McKay said poorer residents are likely to be hurt the most by a property tax rate increase, noting that assessments in low-income areas have risen faster than in wealthier neighborhoods.

“Those are the places where people can least afford to be able to pay and manage that increased cost of housing,” said McKay, a former Lee district supervisor who was elected chairman in November. “We’ve put more money in affordable housing but, on the other hand, increased the tax rate and made housing less affordable. We certainly have to be very cognizant of that.”

Supervisor Pat Herrity (Springfield), the lone Republican left on the board, said the higher tax rate — amounting to an average 5.25 percent increase in mortgage payments — would have a wide impact at a time when wages in the region have remained relatively stagnant. He argued that the county should instead look to cut spending.

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“You look at our homeowners’ salary increases, they’re not going up 5.25 percent this year, at least for most of them,” Herrity said.