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There are **26** NRICH Mathematical resources connected to **Linear functions and graphs**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### The Square Under the Hypotenuse

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Kite in a Square

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's That Graph?

Can you work out which processes are represented by the graphs?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Is Bigger?

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Translating Lines

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### At Right Angles

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Negatively Triangular

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Age 14 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Diamond Collector

Collect as many diamonds as you can by drawing three straight lines.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perpendicular Lines

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Spaces for Exploration

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### Intersections

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Enclosing Squares

Can you find sets of sloping lines that enclose a square?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Electric Kettle

Explore the relationship between resistance and temperature

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Painting Between the Lines

In abstract and computer generated art, a real object can be represented by a simplified set of lines. Can you create a picture using mathematical instructions?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Designs

This task requires learners to explain and help others, asking and answering questions.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Close to Triangular

Drawing a triangle is not always as easy as you might think!

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four on the Road

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spot the Difference

If you plot these graphs they may look the same, but are they?

Age 16 to 18

ShortChallenge Level

Article
Primary curriculum
Secondary curriculum
### Coordinating Classroom Coordinates

This article describes a practical approach to enhance the teaching and learning of coordinates.

Age 7 to 11

Problem
Primary curriculum
Secondary curriculum
### Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

Age 14 to 16

Challenge Level