You calculate the angle of the billiard stick to the ball like this:
var dx = ballX - stickX;
var dy = ballY - stickY;
var angle = Math.atan2(dy,dx);
Then you can move the ball along that angle like this:
var newBallX = ballX + desiredRollDistance * Math.cos(angle);
var newBallY = ballY + desiredRollDistance * Math.sin(angle);
Your desired roll distance would be based on how far the stick was drawn back away from the ball.
The further the stick was drawn back == the further the ball would travel.
You can calculate the distance from the stick to the ball like this:
var dx = ballX - stickX;
var dy = ballY - stickY;
var lengthFromStickToBall = Math.sqrt(dx*dx+dy*dy);
Here is a Demo: http://jsfiddle.net/m1erickson/B6K9z/