Undefined slope v/s zero slope

In mathematics, everywhere, there is an implementation of line. It is implemented everywhere, i.e., in geometry, algebra, and others. The slope defines the line's direction.

In this article, we are going to discuss two types of slopes that are undefined slope and zero slope. Before understanding the types of slope, let's first see the brief description of slope.

What is slope?

The slope defines the steepness of the line. The word 'steepness' means how much the line is slanted. In other words, the slope shows the direction of a line on the coordinate plane. Thus, it is also known as the gradient of a line. Ramp, stairs, etc., are some of the real-life examples of the slope.

In mathematics, the slope is the ratio of "rise" by "run" between two points. "Rise" means the vertical change in the line, and "Run" means the horizontal change in the line.

The slope of a line between two points (x₁, y₁) and (x₂, y₂) can be determined by finding the difference between the coordinates of the points. The slope of a line is generally represented by the letter 'm'.

m = Δx/Δy = (y₂ - y₁)/(x₂ - x₁)
or, m = rise/run

Undefined slope

The undefined slope is the slope of the vertical line. That means if the line is vertical, the slope is undefined. The line in the undefined slope is parallel to the y-axis, and the value of ?x is 0. The x-coordinate of undefined slope never changes no matter what the y-coordinate is. In an undefined slope, the value of Δy is a non-zero integer, whereas the value of Δx is 0. The undefined slope is opposite of the zero slope. In terms of rise and run, the rise in undefined slope is either positive or negative, and run in the undefined slope is zero.

m = Δy/Δx = positive or negative Δy/0

The undefined value of m represents the undefined slope and the vertical line.

In the following graph, you can see the representation of an undefined slope. The line in the below graph is parallel to the y-axis that denotes the undefined slope.

Fig: Representation of undefined slope

In the above image, there is a vertical line which is indicating the undefined slope.

Zero slope

In the zero slope, the line is parallel to the x-axis, and y-coordinate never changes. It is the slope of the horizontal line. In terms of rise and run, the rise in the zero slope is 0, and the run in the zero slope is positive.

m = Δy/Δx = 0/positive Δx

If the value of m is equal to zero, the line is horizontal and has a constant slope.

In the following graph, you can see the representation of zero slope. The line in the below graph is parallel to the x-axis that denotes the zero slope, and y in the zero slope remains the same, no matter what the x is.

Fig: Representation of zero slope

In the above image, there is a horizontal line which is indicating the zero slope.

Now, let's see the difference between an undefined slope and a zero slope.

Difference between Undefined slope and Zero slope

The undefined slope is opposite of the Zero slope. The difference between the undefined slope and zero slope is tabulated as follows -

S.no.	Undefined slope	Zero slope
1.	It is determined by the variable X.	It is determined by the variable Y.
2.	It is the slope of the vertical line.	It is the slope of the horizontal line.
3.	The undefined slope does not have any concrete value, so it has a non-existent value.	Zero slope is a determined value, i.e., Zero.
4.	The denominator of the undefined slope is zero.	The numerator of the zero slope is zero.
5.	In an undefined slope, Y changes, but X does not change.	In an undefined slope, X changes, but Y does not change.

That's all about the article. We have tried to give you sufficient information in an easier way. Hope it is beneficial to you and provide you the information about undefined slope, zero slope, and their comparison.

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