3 or more Lines are said to form a family if either
The lines are concurrent i.e. they pass through a common point of intersection
The lines are parallel to each other
Adding equation of 2 Lines always gives an equation of a Line that belongs to the same family as of original 2 Lines.
Subtracting equation of 1 Line from other also gives an equation of a Line that belongs to the same family as of original 2 Lines. (except in case of 2 parallel lines whose corresponding \(x\) and \(y\) coefficients are same).