Sliding cube around on x/z axis with a constant y-axis

Hi,

I have tried several ways of doing this but I cannot get it right. I'm basically sliding a cube on a plane. The plane is just there for visual effect. I don't want to use a rigid body, etc. I'm using the following code for the dragging:

 void OnMouseDown()
 {
         screenPoint = Camera.main.WorldToScreenPoint(transform.position); 
         offset = transform.position - Camera.main.ScreenToWorldPoint(new Vector3(Input.mousePosition.x, Input.mousePosition.y, screenPoint.z));
     }
 
     void OnMouseDrag()
     {
         Vector3 dragPosition = new Vector3(Input.mousePosition.x, Input.mousePosition.y, screenPoint.z);
         dragPosition = Camera.main.ScreenToWorldPoint(dragPosition) + offset;
         dragPosition.y = 2.0f;
         transform.position = dragPosition;
     }

The cube needs to slide around the screen but remain of a y value of 2.0f. The cube moves on the X and Z axis but I want the y-axis to stay constant on 2.0f, but it goes out of sync with the cursor. Can anyone give me a pointer in the right direction?