**How to Graph Vertical and Horizontal Lines**

The equation of any **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.

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.

So, we can now plot the points in 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 (3, 0).

On the other hand, the equation of any **horizontal lines** come 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.

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 will assume different unique values.

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

Graphing these points in the xy axis, we have a horizontal line parallel to the *x*-axis and passing through the point (0, –2).