What is Horizontal Line? (Definition, Equation, Slope with Examples) - BYJUS

# Horizontal Line

The term "sleeping lines" refers to horizontal lines. Horizontal lines are those that are parallel to the x-axis in a coordinate plane. Horizontal lines can be found on the steps of a staircase or a ladder, sides of a table and other places. Let's look at the properties of horizontal lines, as well as its equation and slope. ...Read MoreRead Less

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## What is a Horizontal Line?

A horizontal line is a straight line with only a y-intercept and not any x-intercept. Hence the equation of a horizontal line is always of the form y = awhere the y-intercept or the y-coordinate of the point the line passes through the y-axis is represented by the letter a.

The following are some examples of horizontal line equations:

• y = 3
• y = -2
• y = -7
• y = 6
• y = 2

## Slope of Horizontal Line

Consider a horizontal line: In a horizontal line the y-coordinate remains the same, only the x-coordinate varies. Hence, any two points on the line can be written as $$(x_1, y)$$ and $$(x_2, y)$$.

Slope of any line, $$m=\frac{y_2~-~y_1}{x_2~-~x_1}$$

$$m=\frac{y~-~y}{x_2~-~x_1}$$

m = 0

It can be seen that horizontal lines have the same slopes as their slope is always zero.

## Horizontal and Vertical Lines

Horizontal lines are parallel to the x-axis and drawn from side to side (left to right or right to left). Vertical lines are parallel to the y-axis and are drawn from top to bottom or bottom to top. Hence, vertical and horizontal lines are always perpendicular to each other.

## Solved Examples on Horizontal Line

Example 1:

Find the equation of the horizontal line that passes through (0, 4).

Solution:

Given:

(0,4) denotes that when the x-coordinate is 0, the y-coordinate is 4. Hence the y-intercept is 4.

A horizontal line’s general equation is y = k where the yintercept is “k”.

Here, the value of k = 4.

As a result, the given horizontal line’s equation is y = 4.

Example 2:

From the image, recognize the horizontal line segments in the shape.

Solution:

The horizontal lines are sleeping lines.

Therefore in the given shape, the horizontal line segments are AB, EF and CD.

Frequently Asked Questions

A horizontal line is one that runs parallel to the x-axis and has the same y coordinate throughout. The horizontal line’s equation is y = b where the coordinates of the y-intercept is (0, b).

A horizontal line has no vertical change, so its slope is zero. On the coordinate plane, a horizontal line is parallel to the x-axis so the y coordinate remains constant throughout. Hence there is no rise in the line. As a result, the horizontal line has no slope.

If an equation if of the form y = b, then we can say that it is a horizontal line that passes through the point (0, b).

If a line is vertical, it will be parallel to the y-axis and will have no y-intercept. Hence a vertical line is of the form x = c, where the line passes through the point (c, 0).