Straight line graphs are also known as linear graphs. There are two different types of linear graphs:

In this section, we are going to be looking at vertical and horizontal graphs.

- Vertical and horizontal graphs
- Upwards or downwards sloping graphs

In this section, we are going to be looking at vertical and horizontal graphs.

**Vertical Graphs**

Verticals lines take the form

*x*= n, where n is a number. With vertical graphs it does not matter what the

*y*value is, because the

*x*coordinate will always be the same (in the example

*x*= n, the

*x*coordinate will always be n, whatever the value of n is).

**Example 1**

Sketch the graph

*x*= 3.

The

*x*coordinate for this graph is always going to be 3. So, when

*y*is 1,

*x*will be 3, which gives us the coordinates (3, 1). When

*y*is -2,

*x*will also be 3, which means that the coordinates are (3, -2) etc…

In order to plot a linear graph, we need to have two coordinates. We plot these two coordinates on a graph and then draw a line that passes through these two points (it is important to continue the line through both of the points rather than just connecting the two points). The graph for

*x*= 3 is shown below.

All of the points that are on the line will have the

*x*coordinate as 3.**Example 2**

Sketch the graph

*x*= -5.

For graphs that take the form of

*x*= “something”, we do not really need to sub

*y*values in. This is because we know that the graph is going to be vertical, so all we need to do is find -5 on the

*x*axis and then draw a line that is perfectly vertical (going up and down from -5). The graph of

*x*= -5 is shown below.

**Horizontal Graphs**

Horizontal graphs take the form

*y*= k, where k is a number. With horizontal graphs it does not matter what the value is for

*x*because the value for

*y*will always be the same. The value for

*y*will be whatever the value for k is.

**Example 3**

Sketch the graph

*y*= 4.

When

*x*is 1,

*y*will be 4, which gives us the coordinates (1, 4). When

*x*is 5,

*y*will also be 4, which gives us the coordinates (5, 4). We now have two coordinates and as the graph is linear, we can draw a line that passes through both of these points. The graph

*y*= 4 is given below.

**Example 4**

Sketch the graph

*y*= -1

For graphs that are

*y*= “something”, we do not need to sub

*x*values in to find the coordinates. This is because we know that the graph is going to be horizontal and that the

*y*coordinate will always be the value of the “something”, which in this question, the

*y*value will always be -1. Therefore, we can find the point on the axis where

*y*is -1 and draw a horizontal line to the right and left. The graph of

*y*= -1 is shown below.

**Finding the Equation of Vertical and Horizontal Lines**

The first step in find the equation of a vertical or horizontal line is to determine whether the line is vertical or horizontal. The next step depends on whether the line is vertical or horizontal:

- If the line is vertical, we know that the equation will take the form
*x*= n. We find the value of n by looking for the*x*value where the line passes through the*x*axis. - If the line is horizontal, we know that the equation will take the form
*y*= k. We find the value of k by looking for the*y*value where the line passes through the*y*axis.

**Example 5**

Find the equation of the line on the graph below.

This is a vertical line, which means that the equation will take the form

*x*= n. The value of n is the*x*coordinate for where the line passes through the*x*axis. This line passes through the*x*axis at -2, which means that n is -2. Therefore, the equation for the line is*x*= -2.**Example 6**

Find the equation of the line on the graph below.

This is a horizontal line, which means that the equation will take the form

*y*= k. The value of k is the*y*coordinate for where the line passes through the*y*axis. This line passes through the*y*axis at -3, which means that k is -3. Therefore, the equation for the line is*y*= -3.