Gradients

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

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

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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