One of the accepted truths of the putting stroke is that the putter should travel straight back and straight through. Any attempt to do this can only be done by manipulating the forearms or the wrists. Now under pressure that type of stroke will never hold up. What the putter should do is just like the full swing, as the club swings up it moves up the incline plane which means it has to be coming up the inside. This is going to give the appearance of the club traveling on an arc.
How to Putt on an Arc
What I have done is set up a rod taped between two stakes in the green. This exercise works very well at home if we take a rod like a broom handle and just rest it across two chairs. Now the idea is that I am going to rest the shaft of the putter against the rod that is parallel to the ground and I am going to practice swinging back and through running the shaft against the rod.
Difference Between Straight Line and Arc in Putting
So the straight line is going to be at any point on the plane but the stroke travels to the inside on the backswing back down the line through impact and then back to the inside on the follow-through. Any attempt to do anything else is going to be filled with complexities that add up to a lot more putts than you need.