What are Vertical Lines? (Definition & Examples) - BYJUS

# Vertical Line

A vertical line is perpendicular to the surface or another line that serves as the base. Vertical lines in coordinate geometry are perpendicular to the horizontal lines and parallel to the y-axis. A vertical line is always a line that runs from top to bottom, or, from bottom to top. Standing lines are also a type of vertical line that runs vertically. We usually draw vertical lines between the bases of a trapezoid or a parallelogram....Read MoreRead Less

## About Vertical Line ## What is the definition of a Vertical Line?

Vertical lines can be found in our daily lives in the form of steel fence rails, tall trees standing upright, table legs, and so on. Let’s learn more about such lines.

A vertical line is a line parallel to the Y-axis in a coordinate plane. The x-coordinate for any point along this line will be the same. The coordinate points of vertical lines are, for example, represented as (5, 0), (1, 0), (- 4, 0), and so on.

A horizontal line, on the other hand, is a line that runs from left to right, or, right to left and is parallel to the x-axis.

## Vertical Line Equation

Vertical lines run parallel to the y-axis, so their slope isn’t defined. As a result, the equation of the vertical line crossing the x-axis at any point ‘a’ is:

x = a

Where, x is the coordinate of a point on the line and a is the point at which the line crosses the x-intercept. The difference between vertical and horizontal lines is illustrated in the image below. The left side of the above diagram depicts vertical lines in a coordinate plane, while the right side depicts horizontal lines parallel to the x-axis.

## Properties of Vertical Line

• The vertical line is parallel to the y-axis, the vertical line’s equation does not have a y-intercept.

• A vertical line’s equation is always written as x = a, with a denotes the x-intercept.

• A vertical line’s slope is undefined. The denominator of the slope is zero because the x-coordinates do not change.

• In math, the vertical line is used to determine whether a relation is a function.

## Solved Vertical Line Examples

Example 1: If Alison travels along a straight line that is denoted by the equation x = 6.  Then create a graph to display this.

Solution:

x = 6 is a vertical line parallel to the y-axis that passes through the x-axis at a distance of 6 units to the right of the origin. Example 2: In the graph below, find the equation for the vertical line. Solution:

We need to figure out what the coordinates are in the graph.

The coordinates of the point are (– 4, 1).

As a result, the equation of the vertical line is:

x = – 4   or   x + 4 = 0

Example 3: What is the slope of a line with equation x = – 7?

Solution:

A vertical line is represented by the equation x = – a.

The slope of a vertical line is undefined, as we all know.

Hence, the vertical line x = – 7 has an undefined slope.