# Family of straight lines

A **family of intersecting straight lines**, is the set of infinite straight lines that pass through a point* P(p _{1},p_{2})*:

Example: y – 3 = m (x – 2), m Є R, is the family of lines that pass through the point (2,3).

A **family of parallel straight lines**, is the set of infinite straight lines that are parallel to a line *r : Ax + By + C = 0:*

Example: 3x + 2y + k = 0, k€R, is the family of lines that are parallel to 3x + 2y – 15 = 0

**Exercises**:

1.- Find the equation of the line that passes through the intersection point of lines *r: 3x + y - 1 = 0* and *s: x - y + 5 = 0* and is parallel to *x + y = 0.*

2.- Find the equation of the line that passes through the points (3,3) and (-1,-1), by using the family of intersecting straight lines of one of them.

Solutions: a) x + y -3 = 0; b) y - 3 = 1·(x - 3)

Licensed under the Creative Commons Attribution Non-commercial Share Alike 3.0 License