A week after officials in Arlington County did the same, the Fairfax County Board of Supervisors on Tuesday endorsed plans for a Columbia Pike streetcar line that supporters hope will become the first leg of a new Northern Virginia rail system.

The 7 to 2 vote was the last action needed for the two counties to apply for federal money that could cover about a third of the construction cost — an estimated $246 million.

But the project isn’t a done deal, as many details have to be ironed out, including who will pay for what.

Years in the works, the counties’ plans call for a five-mile line, akin to light rail, that would run along Columbia Pike from Fairfax’s Skyline area, in the eastern part of the county near Route 7, to the Pentagon City Metro station.

Supervisors expect that the line will spur redevelopment in an area that desperately needs it — Baileys Crossroads — and ease traffic on one of the busiest commuter routes in the region.

According to Fairfax County officials, the corridor has the highest bus ridership in Northern Virginia.

And there are greater ambitions for the Columbia Pike line — that it will become part of a rail network that would extend across the counties and into other jurisdictions.

“We need to get it to Skyline, prove its viability, and then expand it,” said Supervisor Penelope A. Gross (D-Mason), whose district includes Fairfax’s part of the route. “This has a lot of potential.”

Gross has advocated a streetcar line along Columbia Pike for years. She said the need dates back to the 1970s, when a development boom hit the area in anticipation of a Metro stop that was not built.

Even with Tuesday’s vote, it could be years before streetcars are operational.

The two supervisors who voted against the plan, Pat S. Herrity (R-Springfield) and Michael R. Frey (R-Sully), said the cost is too high, especially given other transportation needs that the county has not funded.

They said they are not confident that the project will win the federal money or that the $246 million price tag won’t go up considerably.

“I just don’t see how we can take on another huge capital expense like this,” Frey said.

Supervisor Catherine M. Hudgins (D-Hunter Mill) said she doesn’t see how the county cannot make the investment. “We have to find a way out of the transportation nightmare we’re in,” Hudgins said.

Supervisor Linda Q. Smyth (D-Providence) abstained because her family owns property near the planned route, she said.

The Arlington County Board’s vote last week was 4 to 0, with one abstention.

There was no public comment time during Tuesday’s meeting in Fairfax, but many people have criticized plans for the streetcars.

Opponents have argued that besides being too expensive, the system will take too long to build and could impinge on bicyclists. They have advocated more and better buses.

Supporters say buses won’t be enough as the area grows, and they point to surveys in which 60 percent of respondents said they would not take a bus and would always choose to drive if buses were the only alternative.

In all, the line would have 19 stops, with three in Fairfax County, all of them in the Baileys Crossroads area. Officials said fares would be about the same as for buses.

What has yet to be determined is how the project would be paid for. Fairfax officials said they hope that federal money will cover about $74 million and that the state will chip in $34 million. That would leave Arlington and Fairfax counties with about $138 million to pay.