PINE BLUFF, Ark. (AP) — Michelle Obama told graduates Saturday to prepare to overcome adversity, building on Martin Luther King Jr.’s 1958 commencement address at the same university, when he told students to summon their courage to fight segregation.

The first lady gave an impassioned speech to 270 graduates of the University of Arkansas at Pine Bluff that referenced the legacy of their historically black school, which opened in 1873 with seven students, most of whom could barely read.

Obama said those first students, only a decade removed from slavery, had no guarantee of opportunity once they graduated.

‘‘Let’s just imagine how those seven students would feel if they could see you here today,’’ Obama told a packed downtown arena.

She singled out Quinna Childress of Newport, who graduated Saturday with a 3.935 grade-point average in biology and plans to attend medical school. Childress was homeless at age 16, a high school student living out of a car who worked nights and weekends as a nurse’s aide.

One day at work while contemplating quitting her job, Obama said Childress thought about the lot of her patients who were struggling to overcome illness.

‘‘They needed me more than I needed to give up,’’ Obama quoted Childress as saying.

Obama said Childress’ hardships would add depth to her sense of compassion as a physician.

‘‘It’s going to make her an extraordinary doctor,’’ Obama said.

Obama, a product of Chicago public schools who went on to attain degrees from Princeton and Harvard, said she encountered people in her youth who doubted she could succeed.

‘‘Even today … I know that for some of you this journey has not been easy,’’ Obama said. ‘‘Like me, you wanted something more, right? Just like those (original) seven students.’’

King spoke at the Arkansas campus after he had been arrested and tried for his work; his home had been bombed and his life was threatened. Obama noted that the late civil rights leader’s Pine Bluff address contained phrases he later used in his ‘‘I Have a Dream’’ speech, quoting his refrain, ‘‘Free at last, free at last,’’ as Saturday’s audience roared.

King’s Arkansas speech came a year after federal troops protected nine black students attending all-white Little Rock Central High School. Michelle Obama’s speech came more than a year after the university’s 260-piece band marched in the inaugural parade for her husband, the nation’s first black president.

People in the audience said they hope her appearance draws more attention to historically black colleges.

The Pine Bluff school’s director of bands, John R. Graham Jr., was pulling double duty Saturday. His daughter was getting her chemistry degree while he conducted 170 musicians from the wind symphony and concert band.

Graham said students from across the country seek out his university because they want to attend a traditionally black college. The band has students from as far as California and Florida as well as neighboring states, he said.

‘‘She (Obama) is reaching out to a lot of states by doing this,’’ Graham said.

Betty Scull of Little Rock was on hand with relatives to see her nephew, Brandon Glymph, graduate with a degree in business administration. He’s the seventh member of their family to earn a degree at the university, Scull said.

Scull, an alumna of the Pine Bluff school, was the first in her family to graduate from college, and said the faculty helped her succeed. She went on to earn two advanced degrees.

‘‘There were teachers who believed in me when I didn’t believe in myself,’’ she said.