There are **22** NRICH Mathematical resources connected to **Linear functions and graphs**, you may find related items under Coordinates, Functions and Graphs.

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?

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

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.

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

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

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

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

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

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

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

Can you make sense of the three methods to work out the area of the kite in the square?

Explore the relationship between resistance and temperature

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

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 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?

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

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

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

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

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

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.

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