Slack's public service career began in 1948, when he became a member of Kanawha County Court, where he sat until 1952.

When three-term 6th district Representative Robert Byrd decided against seeking re-election in order to run for the U.S. Senate, Slack won the Democratic nomination and was easily elected that November.

[4] Slack served until his death of a heart attack in Alexandria, Virginia on March 17, 1980.

[5] He was replaced by John G. Hutchinson, then mayor of Charleston, after a special election, who served until the end of the term.

He was interred in Cunningham Memorial Park, St. Albans, West Virginia.