People Express Airlines reportedly has paid a record $1.75 million for landing rights at Washington's National Airport.

The price paid by the low-fare airline for five slots--as landing rights are called--is said to be the highest amount per slot paid to date. Sources said that the seller was Altair Airlines, which is also to receive three slots at Boston in the transaction. People Express is to get the slots--its first at National--on Aug. 1.

People's officials declined comment yesterday on the transaction and on plans for their use of the slots. However, the Newark-based airline is likely to begin its brand of low-fare service from Washington to Newark in competition with New York Air. People's has eliminated ticket counters, airline food and the "free" baggage check-in and pick-up provided by other carriers. Passengers can buy beverages on board and can pay extra to check luggage.

The People-Altair deal was made under a four-week program initiated last month by the Federal Aviation Administration that gave airlines authority to trade, buy and sell slots at 22 major airports whose operations have been restricted since the air traffic controllers strike began last August. The FAA has extended the program for two more weeks but has proposed ending it on June 24.

Aviation sources said that slots at other airports are being sold at prices significantly lower than those at National. Besides the air traffic control limitations on National, Washington's close-in airport also is restricted by the government's National Airport Policy, which limits annual passenger traffic and flights per hour and places a curfew on operations to encourage use of the area's other airports.

Sources said prices of landing rights have been in the $200,000 range at Denver and Chicago; about $100,000 at Los Angeles, Houston and New York's LaGuardia; and $50,000 at Dallas. A government official said yesterday that United Airlines so far has been the biggest buyer of slots, garnering 25 at four airports.

People Express, whose formation was made possible by the Airline Deregulation Act, began service a little over a year ago with three planes to four cities. Now, with a fleet of 17 Boeing 737 jets, it provides service to 12 cities. It flies nonstop from Baltimore/Washington International Airport to Newark, Palm Beach, Sarasota and Melbourne.

The airline suffered a net loss of $1.9 million in the first quarter of 1982, but an operating profit of $184,000. Last week it reported that it carried almost a quarter-million passengers in May, filling 62.8 percent of its seats. In April it operated at a 68.2 percent load factor.

In another development, Squadron Aviation, an air taxi service based at Dulles International Airport, has formed Americair Inc., in order to begin commuter service between the area's three airports. However, the venture faces significant startup problems. Squadron President David Sullivan acknowledged that the most challenging problem the firm faces is gaining slots for the new service; he is talking to FAA officials now, he said.

If slots can be acquired, Sullivan said their proposed Federal Shuttle would operate from Dulles to National to BWI, then back from BWI to National to Dulles. The shuttle initially would operate five round-trip flights a day using an eight-passenger, twin-engine Britten-Norman Islander the firm is negotiating to buy, he said. Current plans call for a $20 fare between National and Dulles, a $30 fare between National and BWI and a $40 fare between BWI and Dulles.

Squadron is a privately owned company that has been in business three years.