President Reagan kicked off the final campaign swing of his political career yesterday with a visit to Boston and a call to Democrats and younger voters to join him "down that path of hope and opportunity."

Speaking before a selected crowd of more than 15,000 at City Hall Plaza and thousands more listening behind a wooden fence, Reagan repeatedly courted younger voters, who made up a large and vocal part of the audience.

"Your generation really sparkles," Reagan said of younger voters, who have turned out enthusiastically for the President across the country. Yesterday's crowd responded with raucous chants of "Four More Years," "Mondale Sucks," and "U.S.A., U.S.A."

"We have a sacred trust and that is when the time comes to turn over the reins to you young people out there, that we turn over to you an America that is every bit as full of opportunity, hope, and confidence and dreams as we knew when we were your age," Reagan said near the end of his half-hour stump speech.

Reagan several times had to respond to hecklers, who booed him when he quoted John F. Kennedy '40 and held aloft signs reading "KKK for Reagan," "Boston Hates Ron," "Reagan Hypocrite," and "Vote for Reagan; You won't live to regret it."

Reagan responded to one loud out break with a retort that has served him well on the trail. "There's one particular group here, and if they keep on yelling. I'm going to raise their taxes," Reagan quipped after his claim that he had cut taxes equally for all Americans was greeted with some jeers.

The President, surrounded by dozens of top New England Republicans and conservative Democrats--including former Gov. Edward J. King--tailored many of his remarks to lure voters away from the Democratic Party, which holds a 4-to-1 edge in voter registration here.

"I know there are millions of good patriotic Democrats who can no longer follow the leadership of that party," Reagan said. "I say to all of them and all of you who are here today, come on and let's--in a bipartisan tradition that is the glory of this country--keep this United States free and strong for all of us."

Except for opening remarks delivered specifically for the Boston audience, Reagan delivered his basic stump speech, which included a celebration of the Grenada invasions, criticisms of Mondale's tax plan, and a description of how life has improved since the economic recovery.

"We knew that economic freedom meant paying less of the American family earnings to the government, so we cut taxes across the board by 25 percent," Reagan said. He was referring to his 1981 tax cut package, which resulted in large tax breaks for the wealthy and a small increase in taxes for those in the low-income range.

Coattails Dragging

The rally sets the stage for a spectacular finish to the Presidential and Senate races in the Bay State. Today, challenger Walter F. Mondale will try to draw even larger crowds at a heavily-promoted noontime rally near the Park Street station on the Boston Common.

His visit must have a strong impact if it is to offset the President's appearance today. He will also have to give a push to Democratic Senate candidate Lt. Gov. John F. Kerry, whose lead over Republican Raymond Shamie has not grown despite charges that Shamie is connected to the John Birch Society and may shrink after today's Reagan endorsement.

The Reagan visit, his first since January, 1983, is seen as a sign that he is confident enough of victory to venture into what once was alien territory.

He narrowly won the state in 1980, but his 41.9 percent plurality was his third lowest percentage total in the country. This year, he had reportedly largely conceded the state to Mondale until recent polls showed him equal to or ahead of his Democratic challenger.