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.
Horizontal Line Examples
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Example 1: Determine which of the following is/are a one-one function.
a) f(x)=x3
b) g(x)=x2
c) h(x)=|x|
d) k(x)=ln x
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.
In the given functions, 'f' and 'k' have only one point of intersection with the horizontal line, hence, they are one-to-one.
Answer: Only f and k are one-to-one.
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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
Answer: y = 3.
FAQs on Horizontal Line
What is Meant by a Horizontal Line?
Horizontal lines are lines that are parallel to the ground (or horizon). In coordinate geometry, horizontal lines are 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 the slope of a horizontal line is equal to zero.
Does a Horizontal Line Have a Slope?
No, the slope of a horizontal line is zero. The slope of a line is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Since the y-coordinates of any two points are the same on a horizontal line, the numerator of the slope formula is zero. Hence, the slope of a horizontal line becomes 0.
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:
- Plot a random point on the coordinate plane, let's say at (1, -5).
- Note down its y-coordinate. In this case, it is -5.
- Plot a point whose y-coordinate is -5, say (0, -5).
- Join both 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 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?
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 points like (0, 5), (-1, 5), (6, 5), etc.
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's slope is zero, as there is no difference in the y-coordinates.