Economics, 3rd Edition

Linear Equations 

During your course it is likely that you will have to work with linear equations – equations 

which are represented graphically as straight lines. A linear equation typically looks like:

y = a + b

 

x

In this equation, 

y = the value plotted on the vertical axis (the dependent variable) and x is the value on 

the horizontal axis (the independent variable).

a is a constant and represents the point where the line cuts the 

y axis and b is the slope of the line 

or its gradient. We can plot a linear equation as a graph by assigning different values to 

x and using the 

equation to establish the value of 

y in each case. This is represented in the table for Figure 2A.1 for the 

linear equation 

y = 5 + 2x.

Values of 

x

 and 

y

 for the linear equation 

y = 5 + 2x

 between 

x = 0

 and 

x = 10

 when

x

y = 5 + 2x

 

y

0

y = 5 + 2(0)

  5

1

y = 5 + 2(1)

  7

2

y = 5 + 2(2)

  9

3

y = 5 + 2(3)

11

4

y = 5 + 2(4)

13

5

y = 5 + 2(5)

15

6

y = 5 + 2(6)

17

7

y = 5 + 2(7)

19

8

y = 5 + 2(8)

21

9

y = 5 + 2(9)

23

10

y = 5 + 2(10)

25

0

5

10

15

20

25

30

0

1

2

3

4

5

6

7

8

9

10

y

x

Graph of 

y = 5 + 2x

V l

f

d

f

h

FIGURE 2A.1

Notice that the line intersects the vertical axis where 

x = 0. The value of the constant a in this equation 

is 5 and represents the vertical intercept, the point where the equation of the line cuts the vertical axis. 

Next thing to notice is that as we give different values for 

x we see that the value of y rises by 2 for each 

increase of 

x by 1. In the equation, the constant b is 2 and is the slope or gradient of the line. More on 

slopes later in this appendix.

Types of Graphs 

The line graph we generated from the equation is one example of a graph that you will 

use in your study of economics. There are a number of others.

Why use graphs at all? Graphs serve two purposes. First, when developing economic theories, graphs 

offer a way to express visually ideas that might be less clear if described with equations or words. Secondly, 

when analysing economic data, graphs provide a way of finding how variables are in fact related in the 

world. Whether we are working with theory or with data, graphs provide a means by which we can see 

patterns and relationships. Choosing the appropriate graphical method is important – the aim is to make 

the information we are trying to view as clear as possible. An effective economist chooses the type of 

graph that best suits the purpose at hand.