Fairfax County’s board of supervisors Tuesday formally adopted a 2016 budget that keeps the property tax rate for homeowners the same, but falls $14 million short of what county schools were seeking to meet growing expenses.

The board had already approved the nearly $4 billion spending plan last week, making Tuesday’s 8-2 vote a formality that ends a process of public hearings and committee meetings that began when county executive Edward L. Long introduced his budget plan in February.

“This is a formality to make sure that all of the ‘T’s’ are crossed and the ‘I’s’ are dotted, and that everything adds up correctly,” board chairman Sharon Bulova said before the vote.

Most of what Long proposed was kept intact by the board in a year when the region’s still weak economy has led to lower commercial tax revenues and the highest office vacancy rate since the early 1990s.

The budget keeps the county’s rate on residential taxes at $1.09 per $100 of assessed value. However, it raises the rate in a special tax district for Tysons Corner by a penny to $0.05 per $100 of assessed value.

Funding for county schools remains at the roughly $2 billion proposed by Long — a $66.7 million increase over this year’s school transfer by the county.

The county’s 12,000 employees will receive cost-of-living raises of 1.10 percent — which is short of the actual 1.68 percent increase in the cost of living from last year.

Both Supervisors Pat Herrity (R-Springfield) and Linda Smyth (D-Providence) voted against the plan.