Vertical line (Coordinate Geometry)
 
Definition: A line on the coordinate plane where all points on the line have the same x-coordinate.
Try this Drag the points A or B and note the line is vertical when they both have the same x-coordinate.

A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane. All points on the line will have the same x-coordinate. In the figure above, drag either point and note that the line is vertical when they both have the same x-coordinate.

A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. As you drag the points above, notice that the slope indicator goes away when the line is exactly vertical.

The equation of a vertical line is

x = a Where:
x is the coordinate of any point on the line
a is where the line crosses the x-axis (x intercept).
Notice that the equation is independent of y. Any point on the vertical line satisfies the equation.

Examples

Fig 1. Is the line vertical?
Determine if the line shown in Fig 1 is vertical and write its equation.

The points A and B on the line are at (-15,3) and (-15,20). The first coordinate in each pair is the x-coordinate which are -15, and -15. Since they are equal, the line is vertical.

Since the line crosses the x-axis at -15, the equation of the line is

x = -15;
which can be read as "for all values of y, x is -15".

Things to try

  1. In the figure at the top of the page, drag the points around and note how points on vertical lines can have any y-coordinate, but the x-coordinates are the same.
  2. Click "hide details". Adjust the points to create a new vertical line. Write down the equation of the line and then click "show details" to verify your answer.

Limitations

In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place. This can cause calculatioons to be slightly off.

For more see Teaching Notes

Other Coordinate Geometry entries