The putter moves on an arc, that arc can be determined by subtracting the lie angle of your putter from 90 degrees. If you look at a plane, the base of the plane is straight but as the putter moves up and in on the backswing and follow through the arc is created.
Pictured the 18 degree Visio Mat showing the arc of the putter head travel. A plane board is also resting at a 72 degree angle, the base of this plane is straight but the putter moves up and in as it travels back and through. Depending on what you are looking at you could say the putter moves straight back and through or in an arc. I describe the arc to my players.
Gripping the putter in the palm of your hand through the lifeline gets the forearms on the same plane as the putter.
Putter in line with forearm in one arm grips righty and lefty.
The first thing you should determine is if a putt is flat, downhill, or uphill. Then pick a spot to account for the ascent or descent.
Every putting stroke should have the same tempo and occur in the same amount of time.
The finish is slightly shorter than the backswing in good putting strokes.