Horizontal and Vertical Line Drawing

Horizontal line

A horizontal line 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.	Horizontal Line Slope
3.	Horizontal Line Equation
4.	Horizontal Line Test
5.	Horizontal and Vertical Lines
8.	FAQs on Horizontal Line

What Is a Horizontal Line?

Horizontal lines are also known as sleeping lines. 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 the railway tracks, etc.

Horizontal Line Slope

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 points 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 the 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 are the same. 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 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. Horizontal lines and vertical lines are perpendicular to each other.

☛ Also Check:

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

Solved Examples on Horizontal Line

1. Example 1: Find which of the following functions have only one point of intersection with the horizontal line?

   a) f(x)=x³

   b) g(x)=x²

   c) h(x)=|x|

   d) k(x)=lnx

   Solution: Let us graph each of these functions and see which of them would pass the horizontal line test. We draw a horizontal line to see how many graphs have at most one point of intersection with the horizontal line.

   

   In the given functions, 'h' and 'g' have two points of intersection with the horizontal line, hence, they are not one-to-one. Thus, they can't have an inverse.
   In the given functions, 'f' and 'k' have only one point of intersection with the horizontal line, hence, they are one-to-one. Thus, f and k have an inverse.

2. Example 2: Find the equation of the horizontal line.

   

   Solution: The given horizontal line passing through the point: (a,b) = (1,3) We know that the equation of a horizontal line passing through a point (a,b) is y = b. Therefore, the equation of the given line is: y = 3

3. Example 3: Find the equation of the horizontal line passing through the point (4,7).

   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 (4,7) the equation is y = (0) x + b

   The line cuts the y-axis at (0,7). Thus the y-intercept is 7.

   Thus b = 7

   The equation of the horizontal line is y = (0)x + 7 ⇒ y = 0 +7

   y = 7 is the required equation of the horizontal line.

   Answer: The equation of the horizontal line passing through the point (0,7) is y = 7

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Practice Questions on Horizontal Line

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FAQs on Horizontal Line

What is a Horizontal Line?

A horizontal line is a line parallel to the x-axis, where the y-coordinates are the same throughout. The y-intercept of a horizontal line is (0,b). The equation of the horizontal line is y = b.

Does a Horizontal Line Have a Slope?

No, the slope of a horizontal line is zero because there is no vertical change on a horizontal line. A horizontal line is drawn parallel to the x-axis on the coordinate plane and the y-coordinate is constant, throughout. There is no rise in the y-coordinates. Therefore, the slope of the horizontal line is zero.

What Is a Horizontal and Vertical Line?

A horizontal line is a line that is parallel to the x-axis of the coordinate plane and its equation is of the form y = b, where 'b' is constant, whereas, a vertical line is a line parallel to the y-axis and its equation is of the form x = b, where 'b' is constant.

How Is a Horizontal Line Drawn?

To draw a horizontal line on paper, use a ruler. Place it parallel to the horizontal edge of the paper and draw a line along the ruler.

To draw a horizontal line on a coordinate plane, use the following steps:

• Place a dot at any random point on the coordinate plane, let's say at (1, -5).
• Identify its y-coordinate. Here, the y-coordinate is -5.
• Plot some other points whose y-coordinate is the same as the point plotted. Let's plot (0, -5), (-2, -5), etc.
• Join all the points to get the horizontal line.

What Is the Equation of a Horizontal Line?

The equation of a horizontal line passing through a point (a, b) is y = b, where 'b' is constant because in the equation y = mx + b, where 'b' 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 = b.

Is a Horizontal Line Drawn Side to Side or Up and Down?

A horizontal line is drawn side to side, parallel to the x-axis of a coordinate plane and it is perpendicular to the y-axis. The up and down line is a vertical line and it is parallel to the y-axis and perpendicular to the x-axis.

What Is Meant by a Horizontal Line?

Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those 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 because the slope is equal to zero.

What Are the Horizontal Lines on the Globe Called?

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

What is The Horizontal Line at 0 Called as?

The horizontal line at 0 is called the horizon.

If the Equation of a Line is y = 5, Then Is it a Horizontal Line or a Vertical Line?

If the equation of a line is y = 5 , then it is a horizontal line. This line is parallel to the x-axis and passes through the point y = 5 at the y-axis.

What Are The Properties of Horizontal Lines?

The horizontal lines are the sleeping lines that run from left to right or right to left. The following are the properties of horizontal lines.

• In a coordinate plane, the horizontal lines are parallel to the x-axis and perpendicular to the y-axis. The y-coordinates are the same throughout, for different x-coordinates.
• The horizontal line slope is zero, as there is no vertical rise in the y-coordinates.

Horizontal and Vertical Line Drawing

Source: https://www.cuemath.com/geometry/horizontal-line/

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