There are several linear dances: west coast swing, salsa, cha cha, rumba, bolero, nightclub two step, even hustle (which can have the appearance of being a circular dance).
A linear dance is one that is danced in a straight line (actually, between two straight lines) or a slot.
When leading a linear dance, it is the leader’s responsibility to move off the slot – sometimes moving across the slot to the other side – so that the follower can remain in the slot. The follower must have a clear path to move along the slot.
It is also the follower’s responsibility to move in a straight path along the slot – a follower should not try to “help” a leader by moving in a curve to the side of the slot (e.g., a pattern such as cross-body).