Horizontal Line - Equation, Definition, Examples, FAQs - Cuemath

Horizontal Line

A horizontal line is a straight line that is parallel to the horizon or the ground. It has zero slope. It is a straight line that is drawn from left to right or right to left and it is parallel to the x-axis in the coordinate plane. In other words, a straight line that has an intercept only on the y-axis, not on the x-axis is called a horizontal line.

The base that we draw for flat shapes is a horizontal line. Let us learn the properties of the horizontal line, its equation, and the slope of a horizontal line.

1.	What is a Horizontal Line?
2.	Slope of Horizontal Line
3.	Horizontal Line Equation
4.	Horizontal Line Test
5.	Horizontal and Vertical Lines
6.	FAQs on Horizontal Line

What is a Horizontal Line?

Horizontal lines are also known as sleeping lines. It has no vertical movement and remains at a constant height from the ground.

In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on railway tracks, etc.

Slope of Horizontal Line

The slope of a horizontal line is zero. While calculating slope = rise/run, we see that there is no "rise" in the y-coordinates as they are the same throughout the horizontal line. Hence there is no change in y coordinates and eventually, the slope of the horizontal line is 0. Let us understand this by drawing a horizontal line on a coordinate plane. Follow the steps to draw a horizontal line on a coordinate plane.

• Step 1: Place a dot at any random point on the coordinate plane, let's say at (2, -3).
• Step 2: Identify its y-coordinate. Here the y-coordinate is -3.
• Step 3: Plot some other point(s) whose y-coordinate is the same as the point plotted. Let's plot (1, -3), (-2, -3), etc.
• Step 4: Join all the points and extend them on both sides to get a horizontal line.

We can see that, there is no change in the y point on a horizontal line. The horizontal line continues straight left or right. The slope of a horizontal line is 0 as by comparing y = b with y = m x + b, we get the slope to be m = 0. Thus, the slope of a horizontal line is 0.

Horizontal Line Equation

Considering the previous image, we can see that the y-coordinates of all the points on a horizontal line is equal to a constant. Thus, the equation of a horizontal line through any point (a,b) is of the form: y = b, where b is constant.

Here x is absent. It means that the x-coordinate can be anything whereas the y-coordinate of all the points on the line must be 'b' only. The y-intercept of the horizontal line is (0, b).

Considering the previous image with points (a, b): (2, -3), (1, -3), (-2, -3), we can see that the y-coordinate of all these points is constant, which is -3. Hence, the equation of this line is y = -3.

Horizontal Line Test

The horizontal line test is used to determine whether a function is a one-to-one function. According to the horizontal line test, a function is NOT one-to-one if there exists a horizontal line that passes through more than one point of the graph (of the function). In other words, in a one-to-one function, there is only one unique x-value for every y-value.

• In the first image, f (x) is one-to-one because every horizontal line passes through at most one point of the graph.
• In the second image, g (x) is NOT one-to-one as the horizontal line that passes through more than one point of the graph.

Horizontal and Vertical Lines

Horizontal means "side-to-side" hence horizontal line is a sleeping line, whereas, vertical means "up-to-down" therefore a vertical line is a standing line. Horizontal lines are lines drawn from left to right or right to left and are parallel to the x-axis. Vertical lines are lines drawn up and down and are parallel to the y-axis. Vertical & horizontal lines are perpendicular to each other.

The differences between horizontal line and vertical line are mentioned clearly in the table below.

Horizontal Line	Vertical Line
Parallel to the ground.	Perpendicular to the ground.
Its slope is 0.	Its slope is undefined.
Its equation is of the form y = b where (a, b) is any point on the line.	Its equation is of the form x = a where (a, b) is any point on the line.
It doesn't move vertically.	It doesn't move horizontally.
It is parallel to the x-axis.	It is parallel to the y-axis.
Examples: straight road, the bottom edge of a rectangle etc.	Example: a tower, a flagpole, etc.

☛ Related Topics

Listed below are a few topics related to horizontal lines, take a look.

• Parallel Lines
• Points and Lines
• Equation of a straight line