Two Prince George's County students, desperate last week for help with their school assignments and frustrated by a busy signal at the county's new Homework Hotline, convinced the telephone operator that she had to break in and declare an emergency. The students, home alone after school with a list of assignments, said the hot line was their only hope.

Since it was established by the county teachers union last week, the hot line has received hundreds of calls from students who said they had no one to turn to for help with homework. A second hot line was started on an experimental basis Tuesday by the county's other, smaller teachers' union at four schools.

The youngsters who have called have asked how to set up quadratic equations, conjugate verbs in French, add and subtract, use dictionaries and figure perimeters in metric measure.

A sixth-grader called for help with messy penmanship. A second-grade boy wanted to know why his teacher didn't assign homework.

"You can call other students and get help, but you don't know if they're right," said Laura Thompson, a senior at Oxon Hill High School, who had called in with a calculus problem. "They don't know any more than you do at best; at worst, they know less. It's nice to have someone who knows."

Thompson and other county students are especially concerned with grades these days since tougher minimum grade requirements have been instituted for participation in extracurricular activities. Last week the school administration reported that 39 percent of high school students were ineligible for those activities because they failed to maintain a C average.

At the other end of the hot line are volunteer teachers who stand watch over four ringing phones at the office of the Prince George's County Educators' Association. They are there to answer questions from 5:30 to 8 p.m. Monday and Thursday nights. The phone number is 568-8900.

"Kids need help with their homework and we want to be there to help," said Marjorie Spirer, a social studies teacher at Crossland High School and organizer of the hot line. "We wanted people to see that teachers do care."

Spirer, a teachers union board member, said students are not supplied answers when they call in, but are given help working through the problems.

The need for the hot line is heightened by the number of latch-key children who cannot turn to parents for help, she said. But even when parents are home, they do not always have the answers at hand.

"I may have graduated from high school, but that doesn't mean anything. That was 15 years ago," said Richard Pickard of Cheverly, whose 11-year-old daughter, Amy, had called in with a math question he couldn't solve.

The hot line concept has been used successfully in many school districts across the country, but in the Washington area, only the District and Fairfax County have them in operation up until now.

The Prince George's County Federation of Teachers, a second, smaller union serving county teachers, opened its Dial-A-Teacher pilot program Tuesday at four county schools.

Federation president Denise Fossett said that program, which operates from 5 to 7 p.m. Tuesdays and Thursdays, may be expanded to all schools by the end of the school year. That number is 736-8777.

In the meantime, PGCEA hot line volunteers have found themselves answering questions from students at private schools and from public schools outside the county.

"We're not going to hang up on anybody," Spirer said. "We're just going to help them."

Each night, the hot line has received about 200 calls, more than half of them about math problems. About 65 percent come from elementary students, Spirer said.

Since opening, the hot line has received an increasing number of calls from high school students stumped by trigonometry, calculus and chemistry. When the teacher on hot line duty is as perplexed by the question as the caller, the homework gets turned over to other teacher volunteers at their homes. They call the students back to help with the problems.

The teachers on duty say that in the long run, they will benefit if more students come to class with their homework done.

"It's in our own interest to have our kids be better students," said Suitland High teacher Carol Phelps, a hot line volunteer. "The kids need help. They just need that extra nudge to contact somebody."