Vertical line is a line which is parallel to Y-axis. Vertical line goes from upward to downward or downward to upward. All points on vertical line has same x-coordinate, as they are equidistant from Y-axis. So, every point on it has the same x coordinate.

## Equation of a Vertical Line

All the points on a vertical line are equidistant from Y-axis. Equation of a vertical line is the same as that of a line parallel to Y-axis. Equation of vertical line is as follows:

Where, a is the distance of the vertical line from Y-axis. If vertical line is at right side of Y-axis, then "a" is positive while if vertical line is at left side of Y-axis, then "a" is negative.

## Slope of a Vertical Line

Slope or gradient of a line is the measure of its steepness. The greater the slope, the steeper or more inclined the line would be. A vertical line is parallel to Y axis and goes exactly straight up or down. Therefore, the slope of a vertical line is undefined. Thus, we can say that:
Slope of a vertical line is infinite or undefined.

## Vertical Line Graph

Vertical line graphs are demonstrated below:

Where, AB is the vertical line which is at a distance "a" at right side of Y-axis.

Where, AB is the vertical line which is at a distance "a" at the left side of Y-axis.

## Vertical Line Test

Let us consider a relation f: A -> B
Where, A is domain and B is range. This relation f is a function, if each value in domain A is associated with exactly one value in range B.
Vertical line test determines if a relation can be defined as a function.

If it is
not possible to draw a vertical line which intersects graph of a relation at two or more points, then that relation is a function.

In the above figure, graph passes vertical test, hence this relation is a function.
If it is possible to draw a vertical line which intersects graph of a relation at two or more points, then that relation is not a function.

In the above figure, graph fails vertical test, hence this relation is not a function.

## Vertical Line of Symmetry

A figure is said to have vertical line of symmetry, if a vertical line is drawn exactly from the middle of the figure. Then, the left portion should be the mirror image of the right portion and vice versa. The figure is said to be vertically symmetric. Following images are examples of vertical line of symmetry:

## Vertical Line Segment

Like any line, a vertical line too has unlimited length. A line segment which is bounded by two points on a vertical line, is called a vertical line segment. Following figure shows a vertical line segment AB:

## Examples of Vertical lines

Given below are few examples related to vertical lines:

### Solved Examples

Question 1: Find the equation and draw a graph of vertical line whose X-intercept is +1 units.
Solution:
Given that X-intercept is +1 units. Therefore, coordinates of a point where line intersects X-axis are (1, 0).
Graph of required line is given below:

Equation of the required horizontal line: x = 1.

Question 2: Draw a vertical line whose equation is x = -5.
Solution:
Given that equation of a vertical line is x = -5.
x-intercept = -5
Therefore, required graph is: