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# Parallel Lines

### Parallel Lines

Parallel lines run in the same direction without ever touching each other, and have the same gradient.

Parallel lines maintain the same distance between each other regardless of how long they are. We can design lines to be parallel through similarities in their equations.

If two lines are **parallel** it means that they have the same steepness. Therefore, if two lines are parallel then their **gradients are equal**.

It's really useful to be able to recognise parallel lines both on a graph, and from their equations. We can also find out whether lines are parallel by looking at a pair of coordinates and comparing to a given line.

What is the value of $p$ if the line joining $(1,1)$ and $(5, p)$ is parallel to $y = 2x -5$?

Similarly, we can find the equation of a parallel line which passes through a particular point by subsituting the coordinates into an equation.

What is the equation of the line which goes through the origin $(0,0)$ and is parallel to $y = -3x -4$?