I might look at the "Line" a bit different than some.
It is an opportunity for the horse to "Follow" the line or rope.
This idea transfers to the ride as the rider asks the horse to change direction (in the beginning) with a direct rein.
This is also a foundation for long line driving which also helps to solve problems when not mounted.
The work is accomplished at the walk or trot in most cases.
This is a 20 month old filly that is being worked and readied for driving.
Notice how the lesson starts and ends.