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# Surprising Transformations

**Can you find an order in which I could have carried out the transformations?**

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Age 14 to 16

Challenge Level

*Surprising Transformations printable sheet*

This problem follows on from Translating Lines and Reflecting Lines.

I took the graph $y=4x+7$ and performed the four transformations shown on the cards below.

Unfortunately, I can't remember the order in which I carried out the four transformations, but I know that I ended up with the graph of $y=4x-2$.

There is more than one way of doing this - can you find them all?

Can you explain why different orders can lead to the same outcome?

**What other lines could I have ended up with if I had performed the four transformations in a different order?**