Correction: An earlier version of this article stated incorrectly that the county is exploring a tiered tax rate so that landowners closer to the heart of Tysons Corner would pay more than those on the periphery. Rather, the county is considering different rates for residential and commercial properties.

Despite strenuous objections from residents, the Fairfax County Board of Supervisors voted 8 to 2 on Tuesday to raise real estate taxes in Tysons Corner to help pay for billions of dollars of new transportation infrastructure — improvements that the county sees as vital to its plan to remake the area into an urban downtown.

The supervisors had wanted to exempt residents from the tax, and they still hope that the Virginia General Assembly will provide a remedy that will allow homeowners to be excluded. But the tax increase, as passed, would apply to all landowners within Tysons.

The new tax district, which covers about 6,000 commercial and residential property owners, is expected to generate $250 million over the next four decades. An exact rate — suggested to be between 7 and 9 cents per $100 of assessed value — will be set when the county adopts a budget in April. The owner of a property assessed at $300,000 would pay between $210 and $270 in additional taxes a year. Landowners will begin paying next year.

Supervisors Pat Herrity (R-Springfield) and Linda Q. Smyth (D-Providence), whose district includes Tysons, opposed the tax hike.

“They feel singled out,” Smyth said of her Tysons constituents. “Frankly, I understand exactly how they feel.”

Fairfax County hopes to transform Tysons Corner into a walkable urban core anchored by the new Metro Silver line.

Supervisors were originally slated to decide the issue in December, but delayed action after a long public hearing at which dozens of residents angrily criticized the increase as unfair. The biggest sticking point has been whether to include homeowners or exempt them.

When members of the county’s planning commission first suggested creating a special tax district as part of a much larger plan for financing billions in Tysons transportation improvements, they recommended trying to exclude homeowners, who make up only a small percentage of Tysons landowners. By fall, though, county officials had taken the exemption off the table, saying they believed state law prevented them from limiting the tax to commercial landowners.

Supervisors were widely expected to approve an across-the-board tax hike last month. But after the contentious public hearing, they again reversed course, saying they wanted to try to work with the General Assembly on legislation that would allow for the residential exemption.

The decision to postpone the vote renewed hope among residential homeowners that they might be excluded after all. But they were given no such guarantees Tuesday.

Smyth said she opposed the tax district because relief for residents is so uncertain. Herrity said he voted no because he doesn’t want to see taxes raised on anyone — residents or businesses.

Supervisors who supported the tax increase said it was the responsible thing to do.

John C. Cook (R-Braddock) called the redevelopment of Tysons the board’s “greatest goal” and one that will provide countless jobs and ensure the county’s future success.

“But we can’t have Tysons without paying for it,” he said.

John W. Foust (D-Dranesville) said that even if no legislative solution is found, residents will be asked to pay only a small, reasonable portion of the costs given the benefits they stand to gain, including increased property values.

Whether or not a residential exemption becomes possible, “this is the right thing to do,” Foust said.

For years, Fairfax has been working on plans to remake Tysons from a sprawling, traffic-clogged office park into a walkable urban center where people live, work and play. The effort culminated with the adoption of an ambitious master plan in 2010, which calls for the area — about 1,700 acres — to be largely rebuilt over several decades around four Metro Silver Line stations that will open this year.

About 18,000 people live in Tysons and 100,000 work there. The county hopes to raise the population to 100,000 residents and 200,000 workers by 2050.

In recent months, Fairfax officials have begun takin g tangible steps toward achieving their vision, including figuring out how to fund more than $2 billion in transportation improvements — public-transit projects, sidewalks, bike lanes, a new grid of streets and a handful of major roads — that planners see as essential for the new Tysons’ success.

Supervisors endorsed a funding plan last year that calls for developers to bear most of the costs, but also includes contributions from existing land owners in the form of the tax district.

While the county has justified the district by saying that all Tysons landowners stand to benefit from the area’s redevelopment, many residents disagree. They argue that the county’s plan for Tysons, at least in the near term, will only mean more construction, traffic and noise for the people who live there, and they have called it highly speculative to suggest that all property values in Tysons will increase.

Many also have criticized the district’s proposed boundaries as too wide. Some expected the boundaries would be scaled back before Tuesday’s vote, but they were not.