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The straight line part 2

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# Parallel and perpendicular lines

Now increase your knowledge of the straight line basics. The following equations are more advanced, but are built on the facts and equations you covered in the previous section. For each, we'll work through an example and show you the thought processes and workings you should produce in the exam. Remember, always show your working to gain full marks!

## Gradients of lines which are perpendicular to each other.

Consider two lines with equations and . If the lines are perpendicular to each other then and if then the lines are perpendicular to each other.

Show that the lines with equations and are perpendicular.

First rearrange each equation in the form

Identify the first gradient:

Identify the second gradient:

Complete the proof:

Hence lines are perpendicular

## Intersection of two lines

Two non-parallel lines will have a common point - the point of intersection!

Find the point of intersection of the lines and

First rearrange one of the lines in the form y = or x =

Substitute this result into the other line

Complete the solving process

Point of intersection is (3,2)

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