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Enclosing Squares

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

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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?

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Weekly Problem 35 - 2007

What is the area of the triangle formed by these three lines?

Parallel Lines

Stage: 3 Challenge Level: Challenge Level:1

It may help to keep one variable fixed and just change the other one:

you could keep the gradient fixed and change the intercept,
or you could keep the intercept fixed and change the gradient.

How do these changes affect the equation of the line?