If your vehicle has run off the road onto the shoulder, you should:

Taking your foot off the gas pedal gradually is the correct choice in this scenario. When your vehicle has run off the road onto the shoulder, it's important to allow the vehicle to slow down naturally without abrupt movements that might lead to loss of control. Easing off the accelerator helps the vehicle decelerate gently, reducing the likelihood of skidding or further destabilizing the vehicle.

In contrast, quickly shifting into a lower gear might cause the wheels to skid or lose traction, especially if the surface is uneven or loose. Braking with heavy constant pressure could lead to a sudden stop, increasing the chance of a loss of control. Applying the emergency brake is typically reserved for situations where you need immediate stopping power, which might not be the best first action when you're on the shoulder trying to regain control. All these alternatives may cause abrupt movements that could worsen the situation, while gradually easing off the gas helps maintain stability.