Does the will to live constitute existentialism?

Existentialism – a philosophical theory or approach that emphasizes the existence of the individual person as a free and responsible agent determining their own development through acts of the will (dictionary).

Please note that I asked “the will to live” not whether an individual determines their lives through the acts of their will. More specifically, I am asking is being responsible the reason a person develops the will to live? Do you live for your children? Do you live for you? Do you live to learn? The nouns are the existential variables which may embrace the will to live.