An across the line backswing would see your golf club pointing right of the target at the top of the backswing, rather than parallel to it.
This position results in poor directional control because if you now swing back down by initiating the movement from your lower body, you will approach the ball very much from the inside of the target line and hit the ball out to the right.
If on the other hand you try to correct this position at the top on your downswing, you will now make an over the top movement where the club head moves over the top of your hands and this will result in the club head approaching the ball from the outside of the target line. You will now have to pull the club head towards the ball and this will result in the club head moving across the target line, rather than directly along it and the ball will be hit left of target.
Achieving the correct club position at the top of the backswing makes it much easier to swing along the target line correctly and hit straight shots. If you are experiencing an across the line position at the top of your backswing, then this is a product of an incorrect takeaway and incorrect use of your wrists. As you swing the club head away from the ball at the start of your backswing, if the club head curves in from the target line too quickly and too low to the ground, you will now be forced to pick the club up with your arms to get it to the top of your backswing, resulting in an across the line position.
To cure this, work on improving your takeaway.
The club head should travel directly along the target line away from the ball and then it should start to rise up from the target line as you hinge your wrists. At hip height, the club should be parallel to the target line and horizontal.
A great drill to help you improve this movement is to stand with your back to a wall. Set up with your backside touching the wall and move the club away from the ball so that your club points directly parallel to the wall but not touching it. Work on getting the club head as high as your hands by the time the shaft is parallel to the wall.
Working on improving your takeaway will see a great improvement with it and then you will be able to rotate your upper body to the top of you backswing and you will see that club becomes parallel to the target line, rather than across it.
This will now allow you to improve your accuracy and hit your golf shots much closer to your target.