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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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?

Perpendicular Lines

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

Diamond Collector

Age 11 to 16 Challenge Level:

In the game below, twenty diamonds have been placed on a grid.

You can enter the equations of three straight lines.
Any diamond that lies on one of your lines counts towards your total.

Try to collect as many diamonds as you can!

Once you've had a go at Level 1, you can click on the purple cog to access the Settings menu and try Levels 2 and 3.