 # Horizontal Line

In coordinate geometry, a line is said to be horizontal if two points on the line have the same Y- coordinate points. It comes from the term “horizon”. It means that the horizontal lines are always parallel to the horizon.

## Horizontal Line Definition The horizontal line is a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system. In other words, the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line. This means that the line that does not touch any point on the X-axis.

## Horizontal Line Equation The equation always takes the form:

y = k, where k is the y-intercept.

It is observed that the horizontal lines have the same slope, so the slope of the horizontal line is always zero.

## Horizontal Line Symmetry

The line of symmetry can be either horizontal, vertical or diagonal. If the line of symmetry is parallel to the horizontal plane, then it is known as the horizontal line of symmetry. We can also find the line of symmetry in shapes also. This means that the line divides the shapes into two parts as mirror images. Some of the examples of symmetry are given here. ## Horizontal Line Test

The test is used to find whether the function is one-to-one. (i.e., injective). For a given function, we can decide whether the function is injective or not, by looking at the horizontal lines that intersect the functional graph. This means that if the line that cuts the graph in more than one point, is not a one-to-one function. And also, this test is performed to find whether the function is bijective (one-to-one correspondence) or subjective (onto function).

## Horizontal Line Segment

It is defined as the part of the horizontal line that is limited by the two points. Those two points are called the endpoints.

### Example

Question: Determine the horizontal line equation, whose y-intercept is (0, 2)

Solution:

Given:

Y-intercept = (0, 2)

We know that,

The general equation of the horizontal line is y=k

Here, “k” is the y-intercept. So the value of k = 2

Therefore, the equation of the horizontal line is y = 2. Visit BYJU’S – The Learning App for more maths-related articles in detail and also watch engaging videos to learn the concepts soon.