Vertical Line

 

A vertical line is a straight line that moves from top to bottom or bottom to top in the coordinate plane. It runs parallel to the y-axis and is defined by the equation x = a, where ‘a’ is the constant x-coordinate. Any point on a vertical line will always have the same x-value.

Let’s understand what is vertical line, how to graph it, and explore solved vertical line examples to strengthen your understanding of vertical line in coordinate geometry.

 

Table of Contents

• What is a Vertical Line?
• Equation of Vertical Line
• Properties of Vertical Lines
• Vertical Line Examples
• Vertical Line vs Horizontal Line
• Vertical Line Test for Functions
• Conclusion
• FAQs on Vertical Lines

 

What is a Vertical Line? 

A vertical line is a line that moves up and down in the coordinate plane. It is parallel to the y-axis and has undefined slope. Unlike horizontal lines, which move from left to right, vertical lines are constant in their x-value.

Examples of vertical lines:

• (3, 1), (3, -2), (3, 4) → All lie on x = 3

• (-4, 2), (-4, -1) → All lie on x = -4
  
  

In each case, the x-value remains fixed - this is the core property of a vertical line.

 

Equation of Vertical Line 

The equation of a vertical line is given as:

x = a

Where:

• x is the x-coordinate of any point on the line

• a is the constant x-intercept value
  This equation means that every point on the line shares the same x-value, and the line is parallel to the y-axis.
  
  

Examples:

• x = 5 is a vertical line passing through 5 units right of origin

• x = 0 is the vertical line passing through the origin
  
  

 

Properties of Vertical Lines

Key properties of vertical lines in coordinate geometry include:

• The equation of vertical line is always in the form x = a

• A vertical line has undefined slope

• It has no y-intercept

• In any vertical line, the x-coordinate of all points is constant

• A vertical line goes top to bottom, not left to right
  
  

These rules make vertical lines easy to identify on a graph.

 

Vertical Line Examples 

Here are some practical vertical line examples to visualize:

Example 1:

x = 8
This is a vertical line that crosses the x-axis 8 units to the right of the origin.

Example 2:

x = -4
Vertical line on the x-axis, 4 units to the left.

Example 3:

x = 3
Passes through x = 3, parallel to y-axis.

Example 4:

x = -5
Vertical line located 5 units to the left of origin.

Example 5:

x = 6
A vertical line at 6 units right of the origin.

Each line runs vertically and maintains a constant x-value.

 

Vertical Line vs Horizontal Line 

A vertical line is always aligned with the y-axis, whereas a horizontal line is aligned with the x-axis.

 

Vertical Line Test for Functions 

The vertical line test is used to determine if a graph represents a function.

Rule:
If a vertical line crosses the graph at more than one point, the relation is not a function.

One intersection = function
More than one intersection = not a function

This test is essential in identifying valid mathematical functions.

Conclusion 

The vertical line is a core concept in geometry and coordinate graphing. It follows the rule x = a, runs parallel to the y-axis, and is useful in various math concepts including function analysis. Whether you’re plotting graphs or checking the validity of functions, the vertical line is a fundamental tool in your math toolkit.

 

Frequently Asked Questions on Vertical Lines 

1. What is a vertical line?

Ans.A vertical line is a line that runs up and down the coordinate plane and is parallel to the y-axis.

2. What is the equation of vertical line?

Ans.The equation of a vertical line is x = a, where ‘a’ is a constant.

3. Is x = 0 a vertical line?

Ans.Yes, x = 0 is a vertical line passing through the origin.

4. What’s the slope of a vertical line?

Ans.The slope of a vertical line is undefined.

5. Is x = -3 a vertical line?

Ans Yes, it’s a vertical line that intersects the x-axis 3 units left of the origin.

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