The Carter administration yesterday abandoned the 5.75 percent price, guideline it had planned for its new wage-price program, and substituted a complex formula that officials say will ultimately allow prices to rise between 6 and 6.5 percent a year.

That development came as, separately, the Commerce Department reported that the nation's economy grew barely fast enough last quarter to keep the unemployment rate from rising - precisely the pace the administration in seeking to help dampen inflation under its forthcoming wage-price plan.

The last-minute change in the price guideline came after officials apparently concluded that the original 5.75 percent would be too tough on some businesses. Officials said the existence of already-negotiated wage settlements and cost inccreases would make it difficult to meet.

However, the move is expected to draw fire from organized labor, which consistently has insisted on full parity in treatment of wages and prices as a condition for its participation in the new guidelines program. Labor leaders already are grousing about Carter's new plan.

The new standards will preserve the intended 7 percent guideline for pay increases. It will apply to all pay hikes, both union and non-union, including executive pay and fringe benefits.

The price guideline will ask firms generally to hold their average price increases companywide to half a percentage point below the corporation's 1976-77 average, roughly the same standard Carter tried to apply in the anti-inflation plan he proposed last April.

Officials say there will be two exceptions:

Where workers sharply moderate their wage demands, companies would be asked to pass on the savings to consumers by cutting back their price increases beyond the half percentage point the administration ordinarily would ask.

What companies find they are facing steep cost increases, the half percentage point standard would not apply. The firms would be allowed to boost their prices enough to cover these increased costs. But the administration would ask them to hold profit margins steady.

Officials insisted yesterday the half percentage point "deceleration" will prove tougher than it looks because prices actually have speeded up this year from the 1976-77 base year. Measured from 1978 levels, the cutback could amount to 1.5 percent or more.

Nevertheless, strategists conceded that the shift will allow prices to rise an average 6 to 6.5 percent in the private, non-farm business sector, rather than the 5.75 percent originally planned. Officials described the 5.75 percent figure as "a planning tool."

The shift came as a surprise to most observers. As late as Thursday night, most officials still were describing the program as including aprice guideline of 5.75 percent. The figure was based on an arithmetical calculation offsetting wage boosts with productivity increases.

Carter is scheduled to announce the new plan in a nationally televised speech Tuesday night. The administration has called in economists and analysts from other economic and statistical agencies to help in getting the program off the ground. Many will start early Monday.

The administration is hoping to hold the growth rate to between 3 and 4 percent for the rest of this year and 1979, to avoid overheating the economy and exacerbating inflation. The inflation rate, which soared to a 10 percent pace last spring, now is running 7 to 7.25 percent.

Yesterday, the Commerce Department announced that the "real" gross national product, or the economy's total output after adjustment for inflation, rose at an annual rate of 3.4 percent between July and September. At the same time, inflation slowed to a 7.1 percent pace.

This third-quarter performance appeared to be the kind the administration needs to avoid inflationary pressure that would strain its guidelines.

The administration is seeking to persuade businesses and workers to hold wage increases to 7 percent voluntarily the rest of this year and next and to hold price increases to 5.75 percent. Most outside observers rate the plan's prospects for success as minimal.

The July-September figures were in line with expectations. Commerce Secretary Juanita Kreps said she was "impressed" with the economy's strength, and predicted that "continued performances such as this will surely drive the economic bears into hibernation."

However, Courtenay M. Slater, the department's ranking economist, said the 7.1 percent inflation rate was still too high, and predicted that the nation could face a recession if President Carter's wage-price guidelines don't work.

Slater's warning was beased on fears by some economists that if the administration on its own does not succeed in dampening inflation, the Federal Reserve Board will try to do so by tightening money and credit in a way that would cause total output to decline.

The Federal Reserve has been raising interest rates steadily since last spring, but so far the actions haven't hurt that much, in part because of recent legislation designed to protect the housing industry. However, many analysts believe further tightening could have an impact.

The 7.1 percent inflation rate last quarter was basically the same as that of the first three months of the year. Inflation rose to a 10.8 percent pace during the second quarter, but much of this stemmed from one-shot increases in food and imports prices.