Horizontal line is a line which is parallel to X-axis on Cartesian coordinate system. Horizontal line goes from left to right or right to left. Since all the points on horizontal line are equidistant from X-axis, each point on it has the same y coordinate.

## Equation of a Horizontal Line

Every point on a horizontal line is equidistant from X-axis. Equation of a horizontal line is the same as that of the line parallel to X-axis. Equation of the horizontal line is given below:

Where, b is the intercept of y. "b" is a positive quantity, if horizontal line lies above X-axis. While "b" is a negative quantity, if horizontal line lies below X-axis.

## Slope of a Horizontal Line

Slope or gradient is the measure of steepness or inclination of a line. The greater the slope, the steeper the line would be. A horizontal line is parallel to X axis and is not inclined. Horizontal line does not rise or fall in any direction. Therefore, horizontal line has no slope. Thus, we can say that:
Slope of a horizontal line is zero.

## Horizontal Line Graph

Horizontal line graphs are shown below:

In the above figure, AB is the horizontal line which is at a distance b above the X-axis.

In the above figure, AB is the horizontal line which is at a distance b below X-axis.

## Horizontal Line Test

Let us consider a relation f: A -> B, where, set A is domain and set B is range.

This relation f is referred as a function, if for each value in domain, there exists exactly one value in the range.
Horizontal line test indicates whether a function is one-one and inverse of a function is itself a function.

Horizontal line test says that, if it is not possible to draw a horizontal line which intersects the graph of a function at two or more points, then the graph is one-to-one.

In the above figure, graph passes the horizontal test. Hence, inverse of this function is itself a function.

If it is possibl
e to draw a horizontal line which intersects graph of a function at two or more points, then the graph is not the graph of a function and inverse of that function is not a function.

In the above figure, graph does not passes the horizontal test. Hence, the inverse of this function is not a function.

## Horizontal Line of Symmetry

A figure is said to have horizontal line of symmetry, if a horizontal line is drawn exactly across the middle of the figure. Then, top and bottom portions are mirror images of each other. Following two images show horizontally symmetric shapes:

## Horizontal Line Segment

Any horizontal line has infinite length. A line segment which is bounded by two points on a horizontal line, is called a horizontal line segment. In the following figure, AB is a horizontal line segment:

## Examples of Horizontal Lines

Given below are few examples related to horizontal lines.

### Solved Examples

Question 1: Find the equation of horizontal line, whose y-intercept is 2 units above X-axis and then, draw its graph.
Solution:
Given that y-intercept is 2 units above X-axis. Therefore, coordinates of a point, where line intersects Y-axis are (0, 2).
The required graph of the horizontal line is given below:

Equation of the required horizontal line is y = 2.

Question 2: Draw a horizontal line whose equation is y = -1.
Solution:
Given that the equation of a horizontal line is y = -1.
y-intercept = -1
Therefore, the required graph of the horizontal line is: