Horizontal Line: Definition, Slope & Equation

The concept of a horizontal line is highly significant in mathematics and is widely applied across many real-life scenarios. We usually apply this concept for mapping graphs, drawing geometric shapes, solving algebraic equations and more. The word ‘horizontal’ is derived from the word ‘horizon’, which is the line where the Earth appears to meet the sky. A horizontal line always goes parallel to the ground or horizon or the X-axis.

In mathematics, a horizontal line is described as a straight line that goes from left to right or right to left. In coordinate geometry, a line is said to be a horizontal line if at any two points it has the same Y-coordinate. The graph of the horizontal line can be plotted in the Cartesian plane. Learning the mapping of a horizontal line on a graph is one of the foundational math skills required for advanced topics as well as for competitive tests.

Table of Contents

• Definition of Horizontal Line
• Equation of Horizontal Line
• Slope of Horizontal Line
• How to Draw a Horizontal Line?
• Horizontal Line Test
• Slope of Horizontal Line
• Difference Between Horizontal and Vertical Line
• Solved Examples on Horizontal Lines
• Frequently-Asked-Questions on Horizontal Line

Definition of Horizontal Line

The horizontal line is defined as a straight line mapped from left to right, and it is parallel to the X-axis in the plane coordinate system. It can also be described as a line that intercepts the Y-axis but doesn’t intercept the X-axis. This implies that a horizontal line does not touch the X-axis at any point. On the other hand, a vertical line is always perpendicular to the horizontal line.  

Example: A horizontal line with the equation y = 3 is represented on the graph below:

Equation of Horizontal Line

A horizontal line is represented in the form of an equation as y = k, where k is the y-intercept. A horizontal line always has the same slope. So, the slope of the horizontal line is always zero.

Here are some of samples of horizontal line equations, such as y = 2

y = -2

y = -4

y = 4

y = 9

Slope of Horizontal Line

In simple words, the slope of a line tells you how much a line rises and falls for every unit point it moves along the horizon. Since a horizontal line is parallel to the X-axis, the slope is zero. 

If we compare the given equation with the equation of line in the slope-intercept form, we get

y = mx + c and y = k 

m = 0

Therefore, the slope of the horizontal line is always equal to zero.

How to Draw a Horizontal Line?

The process of constructing a horizontal line in XY coordinates is quite simple. Here are the steps followed to construct a line: 

1. The first step in constructing a horizontal line is to know the dimension of a point on the line, which is the value of the x & y coordinates of a point.

2. The second step is to locate and mark the point in the XY plane. 

3. The next step is to take the point (x,y) as the reference point and draw a line parallel to the x-axis.

4. A horizontal line is drawn.

To understand each step one by one, let's see some examples below.

Horizontal Line Test

The horizontal line test is a visual method used to determine if a line passes through more than one point on the graph. It is used to determine whether it is a one-on-one function or not. In other words, a function is one-to-one if for every x-value, there exists only one unique y-value.

Difference-Between-Horizontal-and-Vertical-Line

The similarity between horizontal and vertical lines is that both will have a one-variable equation.

Solved Examples on Horizontal Lines

1. Determine the horizontal line equation whose y-intercept is (0, 3).

Solution: Given Y-intercept = (0, 3)

We know that, the general equation of the horizontal line is y = k

Here, “k” is the y-intercept. So the value of k = 3

Therefore, the equation of the horizontal line is y = 3

Horizontal line example: y = 3

 

Example 2: Find the equation of the horizontal line passing through the point (3, 5). 

Solution: The equation of the straight line in the slope-intercept form is y = mx + b

The slope of a horizontal line = 0. ⇒ m = 0

For a line passing through (3, 5), the equation is y = (0)x + b

The line cuts the y-axis at (0, 5). Thus, the y-intercept is 5.

Thus b = 5

The equation of the horizontal line is y = (0)x + 5 ⇒ y = 0 + 5

y = 5 is the required equation of the horizontal line.

Answer: y = 5.

Frequently Asked Questions on Horizontal Line

1. What are the properties of a horizontal line?

Answer: Horizontal lines are lines that are parallel to the horizon or ground. In coordinate geometry, horizontal lines are lines that are parallel to the x-axis and form the equation y = b, where 'b' is constant. As there is no change in the y-coordinate, the slope of a horizontal line is equal to zero.

2. What is the slope of a horizontal line?

Answer: No, the slope of a horizontal line is zero. The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Since the y-coordinates of any two points are the same on a horizontal line, the numerator of the slope formula is zero. Hence, the slope of a horizontal line becomes 0.

3. What is the equation of a horizontal line?

Answer: The equation of a horizontal line passing through a point (p, q) is y = q, where 'q' is constant because in the equation y = mx + q, where 'q' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero; therefore, the equation of a horizontal line is y = p.

4. What is the purpose of the horizontal line test?

Answer: The purpose of the horizontal line test is to determine whether it is a one-on-one function or not.

5. What are the horizontal lines on the globe called?

Answer: Horizontal lines on the globe are called latitudes, and they run parallel to the equator.