Puget Sound Power & Light Co. and Washington Energy Co. said they agreed to a $488 million merger that would create the largest electric and gas utility company in the Northwest.

The merger was unanimously approved by the boards of both companies, they said in a joint statement.American utilities, plagued by slow growth in their home markets, have sought mergers as a way to cut costs and improve earnings. Some have sought acquisitions overseas, particularly in Britain.

Under the agreement, shares in Washington Energy would be swapped for .86 share of Puget Power stock. Based on Wednesday's closing stock prices, the transaction is valued at $488 million, they said.

The merger would generate savings of about $370 million over the next 10 years, nearly half of which would come from about 285 job cuts, representing 8 percent of the combined work force of 3,550 employees, the statement said.

Puget Sound Power & Light is the largest investor-owned electric utility serving Washington state, distributing electric power to 830,000 customers in nine counties.

Washington Energy Co. owns Washington Natural Gas Co., the largest gas distribution utility in the Pacific Northwest, serving 468,000 customers in five counties in western Washington state, including the Seattle area.

Washington Energy, through another subsidiary, also sells natural-gas heating equipment, security systems and energy-efficiency products for the home.

The newly merged company would be based in Bellevue, a Seattle suburb, and would be renamed, although a new name has not been determined.

Puget Sound Power President Richard Sonstelie would serve as chairman and Washington Energy Chairman William Vititoe as president of the new company. The board of directors would consist of up to 15 people drawn from both companies' boards.

The merger, subject to approval by shareholders and regulators, could be concluded in the second half of 1996, the companies said.

Last week two Texas utilities, Houston Industries Inc. and Central & South West Corp., withdrew their $2.77 billion takeover bid for Norweb PLC of Britain after the regional electric company accepted a higher offer from North West Water Group PLC, a British water utility.

Atlanta-based Southern Co. in August agreed to buy South Western Electricity PLC of Britain for $1.8 billion.