Dianne Feinstein, appointed to guide the city after the slaying of George Moscone, turned back a strong conservative challenger to become the first woman elected mayor of San Francisco.

"What this victory means is that the people's voices all over the city are going to be heard," Feinstein told a cheering crowd Tuesday night after Supervisor Quentine Kopp conceded he had lost the runoff election, Feinstein got 102,233 votes to 87,266 for Kopp -- or 54 percent to 46 percent.

As president of the board of supervisors, Feinstein assumed the title of mayor and then was appointed to the post by her colleagues after the Nov. 27, 1978, City Hall assassinations of Moscone and Supervisor Harvey Milk.

In winning the election, the 46-year-old doctor's widow finally gained the office she had failed to win in 1971 and 1975.

Despite Feinstein's solid victory, she may have a difficult time in keeping the allegiance of the liberal coalition of minorities, gays and leftist activists she inherited from Moscone. Kopp won both numerous endorsements and a solid minority vote in the city's more liberal districts, indicating a serious division in Feinstein's base.

Equally significant, according to several political observers, was the "softness" of support shown her in the city's voter turnout. Barely 50 percent of the electorate bothered going to the polls Tuesday, compared to a nearly two-thirds turnout in the last mayoral race.

Feinstein's popularity will be severely tested in the coming months as she deals with a municipal budget deficit projected at nearly $117 million, and the selection of a successor to liberal police chief Charles Gain, forced out of office by Feinstein last summer.

Her decision in the latter issue in particular could affect her strength in the city's gay community, which voted for her solidly in the election despite widespread discontent with her performance the past year.

Kopp forced the runoff when he collected 40 percent of the vote to 42 percent for Feinstein in the Nov. 6 general election.

Feinstein, who picked up President Carter's endorsement late in the race, campaigned against Kopp as a "divisive" force in city politics. Kopp was labeled by opponents as "humorless and a "grouch" tags he attempted to shake off by laughing at them in a commercial.

Although the election was nonpartisan and both candidates are Democrats, Kopp had mounted one of the strongest conservative challenges in recent years.

Feinstein won important support when she got the endorsement of David Scott, an avowed homosexual who came in third in the general election. Authorities estimate 15 percent of the city's 650,000 residents are homosexual.