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 = a, where 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 y–intercept 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.
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).