Final answer:
Lady Macbeth speaks the quoted lines in Shakespeare's play 'Macbeth' to her husband, Macbeth, to emphasize her commitment and to encourage him to follow through with their plan to murder King Duncan.
Step-by-step explanation:
The quote "I would, while it was smiling in my face, Have pluck'd my nipple from his boneless gums, And dash'd the brains out, had I so sworn as you Have done to this" is spoken by Lady Macbeth in William Shakespeare's play, Macbeth. Lady Macbeth utters these words to her husband, Macbeth, to chastise him for his lack of resolve and to persuade him to carry through with their plan of assassinating King Duncan. In this moment, Lady Macbeth is asserting that she would be willing to go as far as to kill her own child if she had sworn to do so, implying that Macbeth should be as committed to fulfilling the promises he has made.