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

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

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

Enclosing Squares

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

If you plot the following lines

$\begin{eqnarray} y &=& 2x + 1\\ y &=& 2x + 4 \\ y &=& -0.5x + 1\\ y &=& -0.5x + 2.5 \end{eqnarray}$

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 $c = 4$]