If the string broke while swinging the ball during the demonstration, the best statement that describes what would happen first is:
The ball would fly in a straight line away from the teacher.
This is because, according to Newton's first law of motion, an object in motion will remain in motion in a straight line at a constant speed unless acted upon by an external force. When the string breaks, the centripetal force that was acting on the ball to keep it moving in a circular path is removed, and the ball will move off in a straight line in the direction it was traveling at the moment the string broke.