Vertical Line
The vertical line is a line that is perpendicular to the surface or another line that is considered as the base. In coordinate geometry, the vertical lines are parallel to the yaxis and are generally perpendicular to the horizontal lines. A vertical line is always a straight line that goes from top to bottom or bottom to top. The vertical lines are also known as standing lines. The lines joining the bases of a square or a rectangle are the vertical lines that we usually draw.
In this article, we will explore the concept of the vertical line and its properties. We see vertical lines in our everyday life in the form of steel rails in a fence, tall trees standing upright, legs of a table, etc. Let us learn more about it with the help of a few examples.
What is a Vertical Line?
A vertical line is a line on the coordinate plane where all the points on the line have the same xcoordinate. While plotting the points for a function x = a, on a coordinate plane, we find that a vertical line is obtained on joining the coordinates. In the image below, L1 and L2 are the two vertical lines. All the points in the L1 have only 'a' as the xcoordinate for all the values of y, and all the points in the L2 have only 'a' as the xcoordinate for all the values of y.
Vertical Line on a Coordinate Plane
Given the coordinates passing through a vertical line, we identify the quadrant in which the points lie. If the coordinates are denoted as (a,b), no matter whatever be the value of y, the x value stays constant throughout. Thus the vertical line passes through the point 'a' on the xaxis for all values of y. The xintercept of a vertical line x=a is the point (a,0).
Example of a Vertical Line
In the graph below, we see that for all the values of y, the x value is only 6. The vertical line is 6 units away from the origin, towards the right, and is parallel to the yaxis. (6,0,),(6,1,),(6,2),(6,4,),(6,8), etc... are all the points that lie on this vertical line.
Vertical Line Equation
The equation of a vertical line is given by x = a, or x = a, where x is the x coordinate of any point on the line and a is where the line crosses the xintercept.
Slope of a Vertical Line
A vertical line has a slope that is undefined. As per the definition of slope, we calculate the slope this way:
m = change in y coordinates/ change in x coordinates= (y_{2}  y_{1}) / (x_{2}  x_{1})
Now, since the xcoordinate remains constant on a vertical line, therefore we have x_{2} = x_{1} = x. So, the slope of vertical line is m = (y_{2}  y_{1}) / (x  x) = (y_{2}  y_{1}) / 0 which is not defined as the denominator is zero. The x coordinates remain the same for all the points on the vertical line and there is no run horizontally. Thus the slope of a vertical line is undefined.
Vertical Line Test
A vertical line is used to find if a given graph is a function. A relation is said to be a function only when a vertical line drawn intersects the graph only at one point. A function can have only one output for every input. The image for every preimage is unique, as per the definition of the function.
Thus if a vertical line intersects the graph at more than a point, then it is interpreted as a function having more than one output, which shows it cannot be a function. In the image below, we can witness that a vertical line drawn to the function y = f(x) is a function, because the vertical line intersects only at a point on the curve, whereas in the circle, the vertical line touches at two points. Thus the circle is not a function.
Properties of Vertical Line
 The equation of the vertical line does not have a yintercept, because the line is parallel to the yaxis.
 The equation of a vertical line always takes the form x = a, where a is the xintercept.
 The slope of a vertical line is undefined. Since there is no change in the xcoordinates, the denominator of the slope is zero.
 The vertical line is used to check whether a relation is a function in math.
Vertical Line of Symmetry
A vertical line of symmetry is the straight line that runs top to bottom dividing the shape into two identical halves. There are 11 alphabets in English that have a vertical line of symmetry: A H I M O T U V W X Y. Below is the isosceles trapezoid which has only one vertical line of symmetry.
Important Notes on Vertical Line
 A vertical line is a straight line perpendicular to the base.
 The equation of a vertical line is x = a, where a is the xcoordinate throughout the line.
 The slope of a vertical line is not defined.
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Examples of Vertical Line

Example 1. What is the equation of the vertical line passing through (11,3)?
Solution:
The equation of the vertical line is given as x = ± a, where a is the xintercept
Here the xintercept is 11.
Thus the equation of the vertical line is x = 11
We rewrite it as x + 11 = 0
Answer: The equation of the vertical line passing through (11,3) is x + 11 = 0.

Example 2. Find the equation of the vertical line in the graph shown below.
Solution:
We need to identify the coordinates as represented in the graph.
The coordinates of the point are (4,1)
Thus the equation of the vertical line is x = 4 ⇒ x + 4 = 0
Answer: The equation of the vertical line is x +4 = 0.

Example 3. What is the slope of the line x = 8?
Solution:
The equation of the line x=a represents a vertical line.
We know that the slope of a vertical line is undefined.
Answer: The slope of the vertical line x=8 is undefined.
FAQs on Vertical Line
What is a Vertical Line?
A vertical line is a line on the coordinate plane where all the points on the line have the same xcoordinate, for any value of ycoordinate.
What is The Slope of a Vertical Line?
The slope of a vertical line is undefined because the xcoordinates are the same. The denominator becomes zero in the calculation of slope as there is no change in xcoordinates.
What is The Equation of a Vertical Line?
The equation of a vertical line at a point (a,0) is x = a. The equation of the vertical line is given as x = ± a, where a is the xintercept.
Does a Vertical Line Have a Slope?
A vertical line cannot have a slope. The slope of a vertical line is undefined.
How is a Vertical Line Drawn?
A vertical line is drawn perpendicular to the baseline or to the flat surface. A vertical line goes from top to bottom or from bottom to top. On a coordinate plane, a line parallel to the yaxis is the vertical line.
What is The Equation of a Vertical Line Passing Through (5,2)?
The equation of a line passing through (5,2) is x = 5.
What is a Vertical Line of Symmetry?
A vertical line of symmetry is the straight line that runs top to bottom dividing the shape into two identical halves.
How Do You Know The Equation of The Vertical Line Passing Through a Point?
A vertical line passes through two points having the same xcoordinates. Each point on a vertical line has the same xcoordinate. If two points have the same xcoordinate, 'a' the equation of the line is x = a. The xintercept of a vertical line x=a is the point (a,0).
What are the Examples of Vertical Line?
A vertical line is a line that is perpendicular to a flat surface on the ground. Flagpost, lamppost, the vertical lines joining the bases in a square or a rectangle are all a few examples of vertical lines.
What is a Vertical Line Test?
A vertical line is drawn on the graph to check if a relation is a function or not, while represented graphically. The vertical line drawn to a function on the graph intersects the curve at only one point.
What is the Difference Between a Vertical Line and a Horizontal Line?
A vertical line is a line that is parallel to the yaxis and a horizontal line is a line that is parallel to the xaxis in a coordinate plane.
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