This is NOT how you set the speed of the motor. That's what the motor1.setSpeed() function is for.
Try this for Backward. Then do the same changes for Forward.
// Y-axis used for forward and backward control
if (yAxis < 470) {
// Convert the declining Y-axis readings for going backward from 470 to 0 into 0 to 255 value for the PWM signal for increasing the motor speed
int motor1Speed = map(yAxis, 470, 0, 0, 255);
int motor2Speed = map(yAxis, 470, 0, 0, 255);
int motor3Speed = map(yAxis, 470, 0, 0, 255);
int motor4Speed = map(yAxis, 470, 0, 0, 255);
// Set Motor A backward
motor1.setSpeed(motor1Speed); //Define maximum velocity
motor1.run(BACKWARD); //rotate the motor anti-clockwise
motor2.setSpeed(motor2Speed); //Define maximum velocity
motor2.run(BACKWARD); //rotate the motor anti-clockwise
motor3.setSpeed(motor3Speed); //Define maximum velocity
motor3.run(BACKWARD); //rotate the motor anti-clockwise
motor4.setSpeed(motor4Speed); //Define maximum velocity
motor4.run(BACKWARD); //rotate the motor anti-clockwise
}