# Gradients

**26**NRICH Mathematical resources connected to

**Gradients**

problem

### Which is bigger?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

problem

### Which is cheaper?

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?

problem

### How steep is the slope?

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?

problem

### Surprising Transformations

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

problem

### Translating Lines

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

problem

### Reflecting 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.

problem

### At right angles

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

problem

### Perpendicular lines

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