You’d think that making a sword travel on a straight plane, especially a horizontal one, would be fairly easy but indeed, it is quite difficult. The technique is further complicated by the position of the hands at the extreme ends of the slash. Once I experienced cutting with a ‘live’ blade, the ‘feel’ of the technique was clearer but replicating it in the absence of a straw bale is difficult and my practice is constantly limited by my concerns about developing tennis elbow and wrist tendonitis.
The horizontal slash is usually at waist height but it can also be at head height. I found a good way to practice was by fixing some string between two points at my waist height and then practicing the slash across this. It is much easier to see variations in the plane of the slash in relation to another horizontal plane.