# Pencil of Lines

## Pencil of Lines

The set of all lines in the same plane that pass through a given point called the centre of the pencil.

### Examples

• Pencil of lines with its centre at the point with coordinates (3, 2) :

• In a Cartesian plane, a pencil of lines passing through a point with coordinates (pq) is a family defined by the equation $$y\space =\space \dfrac{q−b}{p}x + b$$, where b is the y-intercept of each line in the pencil of lines.