Question

What are family of lines?

Answer 1

All lines following a specific criteria are called a family of lines.

For eg.
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.