Nuffield Free-Standing Mathematics Activity Linear graphs

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

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

B Graphs of the form y = x + c 0 1 2 2 3 4 y 1 2 5 3 4 –1 –2 –3 –4 –5 x B Graphs of equations of the form y = x + c y = x + 2

Answers for B y y = x - 1 y = x - 2 x y = x + 3 y = x + 2 y = x + 1 1 1 2 5 3 4 –1 –2 –3 –4 –5 y = x + 3 y = x + 1 y = x - 1 y = x - 2

C Graphs of the form y = mx 0 1 2 -1 y = 3x 3 6 -3 x y 1 2 5 3 4 –1 –2 –3 –4 –5 C Graphs of equations of the form y = mx y = 3x

Answers for C y = 3x x y 1 2 5 3 4 –1 –2 –3 –4 –5 y = -2x y = -3x 1 2 5 3 4 –1 –2 –3 –4 –5 y = -2x y = -3x y = 2x y = 0.5x

D Graphs of the form y = mx + c y = 2x - 1 x y 0 1 2 1 2 5 3 4 –1 –2 –3 –4 –5 - 1 1 3 y = 2x - 1 D Graphs of equations of the form y = mx + c

Answers for D x y y = 2x - 1 1 2 5 3 4 –1 –2 –3 –4 –5 y = 2x + 1 1 2 5 3 4 –1 –2 –3 –4 –5 y = 2x + 1 y = 3x - 1 y = 0.5x - 1

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 = 2x + 1, what do the ‘2’ and the ‘1’ tell you about the graph?