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

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

Kkytha provided a couple of diagrams that helped explain why it is impossible to draw the triangle.