# Families of Lines

## Key Questions

• A family of lines is a set of lines that have something in common with each other.

In brief, we can have two types of families of lines:

1. one where the slope is the same $\to$ keep the slope unchanged and vary the $y$-intercept $\to$ parallel lines

2. one where the $y$-intercept is the same $\to$ keep the $y$-intercept unchanged and vary the slope $\to$ concurrent lines

• 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.