How to Graph Vertical and Horizontal Lines

The equation of a vertical line comes in the form

where $a$ is just a constant

Notice that this equation doesn’t contain any variable $y$ . The absence of $y$ means that it can take any values. Here’s an example.

An Example of Graphing a Vertical Line

Graph the vertical line $x = 3$ .

The equation doesn’t have the variable $y$ which implies that it could assume any numerical values for $y$ . In the table of values, you will see that “ $3$ ” is the repeating value in the column of $x$ while having different values in the column of $y$ .

This is precisely the interpretation of the equation $x = 3$ .

a table with x values of 3, 3, 3, 3, 3 and y values of -2, -1, 0, 1, 2.

So, we can now plot the points on the $xy$ –axis to see how it looks. As you can see, it is a vertical line parallel to the $y$ -axis and passing through the point $\left( {3,0} \right)$ .

a vertical line on the xy axis with plotted points (3,-2), (3,-1), (3,0), (3,1) and (3,2)

On the other hand, the equation of a horizontal line comes in the form

where $c$ is just a constant

This time around, the equation doesn’t have any variable $x$ . The absence of $x$ means that the variable $x$ can take any numerical values while the value of $y$ is being held constant. Here’s an example.

An Example of Graphing a Horizontal Line

Graph the horizontal line $y = - 2$ .

Since we have no $x$ -variable in the equation, it is okay to pair the $y$ -coordinate of $- 2$ with any $x$ -values. When you construct the table of values for this, the $y$ -coordinates will be the same throughout while the $x$ -coordinates can have different values.

Observe, the $y$ -column is populated with the same value of $- 2$ .

a table of values with x values of -2, -1, 0, 1, 2 while with y values of -2, -2, -2, -2, -2.

Graphing these points in the $xy$ -axis, we have a horizontal line parallel to the $x$ -axis and passing through the point $\left( {0, - 2} \right)$ .

a horizontal line plotted on the xy axis passing through the points (-2,2), (-1,-2), (0,-2), (1,-2), and (2,-2)