When hitting a racquetball, it is more efficient to use your biggest muscles. This means rotating your hips, upper torso and shoulders, with your arm going along for a ride.
The racquetball backhand starts by turning your back on the target (front wall) with your arm bent at 90 degrees. Then you simply uncoil your upper body. Your arm remains relaxed and will fly out to an extended position at the point of contact with the ball. You should feel like your motion is accelerating during the entire swing. Completely follow through with your arm until you are completely facing the front wall. A successful backhand stroke is flat and level.
Maintain your athletic position during the entire swing and follow-through. Do not stand up straight at any point during your swing!