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'Parallel Lines' printed from http://nrich.maths.org/

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Alter the positions of the line by moving the points.
How does the position of the line affect the equation of the line?

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Now explore what happens when you have two lines.
Position the lines so that they are parallel to each other.
Try various arrangements.

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What can you say about the equations of parallel lines?

You may want to take a look at Perpendicular Lines after this.