Here's a problem to work at with your graphic calculator or graph-plotting package on a computer.

If you plot the following lines

\begin{matrix} y & = & 2 x + 1 & (1) \\ y & = & 2 x + 4 & (2) \\ y & = & - 0.5 x + 1 & (3) \\ y & = & - 0.5 x + 2.5 & (4) \end{matrix}

the lines will enclose a square.

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

If you are given the equations of two parallel lines

y = ax + b

and

y = ax + c

can you explain how to find the equations of the other two lines that would enclose a square, if you know that one of the vertices is at $(0, b)$ ?

[In the example at the top, $a = 2$ , $b = 1$ and $c = 4$ ]