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Enclosing Squares

Can you find sets of sloping lines that enclose a square?

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Parallel Lines

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

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Perpendicular Lines

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Surprising Transformations

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

Transformation cards

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 $y=4x-2$.

Find an order in which I could have carried out the transformations.
There is more than one way of doing this - can you find them all?
Try to 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?