Thank you very very much!
Yes, colored line is present in first two levels as a lazy (2 days is tough!) soft tutorial, for player to get used to the pathfinding mechanisms. It is easier to see where students collide, and also the second level teaches that colliding head on head does not work, you need a corner for that.
And later on there are no lines, because figuring out where the students will go is part of the puzzle itself :)