Nuffield FreeStanding Mathematics Activity Linear graphs Nuffield Foundation

Nuffield Free-Standing Mathematics Activity Linear graphs © Nuffield Foundation 2011

Linear graphs In this activity you will: • use an equation to calculate values • plot graphs • look for a connection between the numbers in the equation and its graph © Nuffield Foundation 2011 y 0 x

A Coordinates x coordinate The position of a point is given by two coordinates. (– 2, 5 ) y y coordinate (2, 5) 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 1 2 3 – 2 – 3 – 4 © Nuffield Foundation 2011 – 5 (– 2, – 5 ) (2, 5) (2, – 5 ) 4 5 x

B Graphs of the form y = x + c y=x+2 x 0 1 2 y 2 3 4 y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 y=x+2 © Nuffield Foundation 2011 – 4 – 5 1 2 3 4 5 x

Answers for B y y=x-1 y=x-2 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 y=x+3 – 3 y=x+2 – 4 y=x+1 – 5 © Nuffield Foundation 2011 1 2 3 4 5 x

C Graphs of the form y = mx y = 3 x x 0 1 2 y 0 3 6 y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 © Nuffield Foundation 2011 y = 3 x – 5 1 2 3 4 5 x -1 -3

Answers for C y = -2 x y = -3 x y y = 3 x y = 2 x 5 4 y = 0. 5 x 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 – 5 © Nuffield Foundation 2011 1 2 3 4 5 x

D Graphs of the form y = mx + c x y = 2 x - 1 0 -1 y 1 1 2 3 y = 2 x - 1 y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 © Nuffield Foundation 2011 – 5 1 2 3 4 5 x

Answers for D y y = 2 x + 1 y = 2 x - 1 5 4 3 y = 0. 5 x - 1 2 1 – 5 – 4 – 3 – 2 – 1 0 – 1 – 2 – 3 – 4 – 5 © Nuffield Foundation 2011 y = 3 x - 1 1 2 3 4 5 x

Linear graphs Reflect on your work Explain to your partner what the values m and c stand for in the equation y = mx + c. For example, for the equation y = 2 x + 1, what do the ‘ 2’ and the ‘ 1’ tell you about the graph? © Nuffield Foundation 2011