Thanks to Jack Kerouac, William Burroughs meet Joan Vollmer in 1946. After a brief relationship, she became his common-law wife. The couple used a lot of drugs: benzedrine, narcotics, amphetamine, marijuana. Joan was also hosted in a mental hospital in 1946.
In 1949, after being arrested for drugs in New Orleans, Burroughs with Joan and their children, William III, born in 1947, moved to Mexico City. Here, on the 6th september 1951, Joan was killed by William:

In 1951, Burroughs killed Joan after shooting her in the head while playing William Tell.
Burroughs allegedly concidered shooting himself as well.
Right before she was killed, Joan allegedly said, “I can’t watch this – you know I can’t stand the sight of blood.”
The police officially ruled it an accident, and Burroughs never served time for the incident.
In his book Queer, Burroughs wrote: “I am forced to the appalling conclusion that I would never have become a writer but for Joan’s death, and to a realization of the extent to which this event has motivated and formulated my writing.”

source: column, Jennifer Berube