The space on which linear functions are drawn is sometimes called the X-Y Plane, because it is made up of two number lines at right angles – the horizontal numberline (X -axis) and the vertical numberline (Y-axis), and defines a flat 2- dimensional area (a plane). It is properly known as the Cartesian Plane, named by RenĂ© Descartes. You may be familiar with games that use a similar system, like Battleship. Battleship isn’t quite a Cartesian Plane, since it uses letters on the horizontal axis. A game that uses the cartesian plan better is Bug hunt – which requires you to find the shortest path (via “manhattan distance” – you don’t have to understand this, but it is interesting!)

But before we can get to playing with the algebra of lines on a cartesian plane, we need to master some simple algebra first – the algebra of expansion and factorisation. We need to be able to deal with distributive law – the rule for multiplying brackets (1, 2, 3) like this:

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