Horizontal Line 

A line is a straight figure that extends infinitely in all directions without curvatures; it has no width or thickness but length. A horizontal line refers to a special type of line running from left to right, parallel to the horizon.

1.0A Brief Overview of Horizontal Line 

A horizontal line runs parallel to the horizon and is perpendicular to any vertical line. A horizontal line refers to a line that has a slope equal to zero. Thus, this line is neither sloping nor declining, a completely flat line from the origin of its length. This, in turn, disqualifies it from many kinds of lines like the case with a vertical or slanting line.

2.0Key Characteristics of a Horizontal Line

1. Slope: Slope is the steepness or incline of a given line. It is the vertical change (rise) with respect to the horizontal distance (run). Hence, The slope of a horizontal line is always 0, since the rise is 0 for any change in run. On the other hand, the slope of a vertical line is undefined. The slope of a line for given coordinates says (x₁, x₂) and (y₁,y₂) is: 

$Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}$

2. Horizontal line equation: The general equation for any line with coordinates (x,y) and slope m can be given as: 

$y=mx+c$

Since the slope for a horizontal line is 0, therefore 

$y=c$

where c is the constant, the y-coordinate of any point on the line. In other words, points along a horizontal line all have the same y-coordinates while their x-coordinates are all different. It is known as the horizontal line equation.

3.0Horizontal Line and Vertical Line

A horizontal line and a vertical line are always perpendicular to each other and form a 90-degree angle at their intersection. The horizontal line has a slope of 0, while the vertical line has an undefined slope. The relationship is important in geometry, used to define coordinates and graphing functions, and divides a plane into different regions.

4.0Difference Between Horizontal Line And Vertical Line

5.0Horizontal Line Test

A method for determining whether a function is one-to-one is by horizontal line test. If a horizontal line intersects the graph of the function at more than one place, then the function fails to pass the test. This will guarantee that there exists exactly one x-value for each y-value; thus, the function is invertible. If a horizontal line crosses the graph at more than one place, the function fails the test and is not one-to-one; thus, it doesn't have an inverse. This Horizontal Line test is a way to assess the behaviour of functions.

6.0Drawing A Horizontal Line

For drawing a horizontal line, start at any point on a grid or surface. Then, draw a straight line from left to right, keeping it level and not tilting up or down. This line must run parallel to the x-axis, with the same y-coordinate along its length. Let us understand in more detail how to draw horizontal lines with the help of some examples of horizontal lines.

Example 1: Draw a horizontal line that represents the bottom edge of Sarah’s garden, which is at a height of 2 feet above the ground. Label the line with its equation.

Solution: y = 2

Problem 2: Draw the horizontal line representing the x-axis, which passes through the origin (0, 0). Label the line with its equation.

Solution: Let the coordinate for the horizontal line be (0,4) 

The Equation will be y = 4. 

Problem 3: Draw a horizontal line at a height of -3 on a graph. Label the line with its equation.

Solution: y = –3 

7.0Also Read