1. Nuffield Free-Standing Mathematics Activity
Linear graphs

2. 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

3. 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 )

4. 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

5. Answers for B y y = x - 1 y = x - 2 x y = x + 3 y = x + 2 y = x + 1 11 2 5 3 4 –1 –2 –3 –4 –5
y = x + 3
y = x + 1
y = x - 1
y = x - 2

6. 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

7. Answers for C y = 3x x y 1 2 5 3 4 –1 –2 –3 –4 –5 y = -2x y = -3x1 2 5 3 4 –1 –2 –3 –4 –5
y = -2x
y = -3x
y = 2x
y = 0.5x

8. 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

9. Answers for D x y y = 2x - 1 1 2 5 3 4 –1 –2 –3 –4 –5 y = 2x + 11 2 5 3 4 –1 –2 –3 –4 –5
y = 2x + 1
y = 3x - 1
y = 0.5x - 1

10. 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?