All lines following a specific criteria are called a family of lines.
If the criteria is passing through a point (0,0)
Then all possible lines passing through that point are called the family of lines.
If the criteria is have a slope of -1,
Then all possible lines have slope = -1 are its family of lines.
The idea is similar to human families where all our relatives belong to the same family (the criteria) and therefore everyone is a family member.
I hope this helps.