Vertical Line

In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate. For example, (2,0), (3,0) (-4,0), etc. are the points of vertical lines. Similarly, the line which goes from left to right and is parallel to the x-axis is called a horizontal line.

The vertical lines have no slope. It goes parallelly along with y-axis and hence the slope is not defined. Therefore, the equation of the vertical line which crosses the x-axis at any point say ‘a’, is given by:

x = a

where x is the coordinate of a point on the line and ‘a’ is the point where the lines cross the x-intercept. See the below image to understand the difference between vertical and horizontal lines.

Vertical and Horizontal Line

In the above figure, we can see, the left side shows the vertical lines in a coordinate plane whereas the right side shows the horizontal lines parallel to the x-axis.

Let us learn more about Vertical Lines.

Properties of Vertical Lines

  • The equation of a vertical line in the graph, which is parallel to y-axis is x = a.
  • The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero.
  • To check whether the relation is a function in maths, we use a vertical line. It would be a function if all vertical lines intersect it minimum once. This is also called a vertical line test. A graph will be considered as a function if it has only one output y for each input x. Therefore, a vertical line cannot be a function.

Solved Examples

Question 1: Plot the graph for the following:

  1. X = 8

x=8 is a vertical line, that passes through x-axis, at a distance of 8 units on the right of the origin and is parallel to y-axis.

Vertical Line Example -1

 

  1. X = – 4

x=-4 is a vertical line, that passes through x-axis, at a distance of 4 units on the left side of the origin and is parallel to y-axis.

Vertical Line Example -2

  1. X = 3

x=3 is a vertical line, that passes through x-axis, at a distance of 3 units on the right side of the origin and is parallel to y-axis.

Vertical Line Example - 3

  1. X = – 5

x=-5 is a vertical line, that passes through x-axis, at a distance of 5 units on the left of the origin and is parallel to y-axis.

Vertical Line Example - 4

  1. X = 6

x=6 is a vertical line, that passes through x-axis, at a distance of 6 units on the right side of the origin and is parallel to y-axis.

Vertical Line Example - 5

To learn more on Lines and angles, visit BYJU’S.

Frequently Asked Questions – FAQs

What is vertical and horizontal line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

What is the equation of vertical line?

The equation of vertical line is given by: x = a
where x is the x-coordinate of any point on line and a is the crossing point of vertical line on x-axis.

What way does the vertical line go?

A vertical line goes straight from top to bottom and bottom to top in a coordinate plane.

Is x=0, a vertical line?

x=0 is a vertical line that passes through the origin and is parallel to y-axis.

Is x = -3, a vertical line?

x=-3 is a vertical line, that passes through x-axis, at a distance of 3 units on the left of the origin and is parallel to y-axis.

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