In mathematics, the rise or run between any two points on a particular line is termed a Slope. A slope is used to measure the steepness of a particular line. It comprises two points or coordinates. These points are shown by variables, “X” and “Y” letters.

A change in either one of the variables will affect the other and vice versa. The letters “X” and “Y” have two different axes. Lines and points are placed with the help of integers on these axes. These integers could be positive or negative, with zero always at the center of the graph.

Zero always lies at the intersection of these two axes. The concept of slopes is very commonly used. Different areas make use of this concept. Fields like economics, construction, architecture, and so on use this concept.

Fields related to health and trend analysis also use the concept of slope in their day-to-day activities. Anything which makes use of an angle or steepness can be measured through the formula for the slope. In most cases, a slope is expressed in positive or negative integers.

In a few cases, the value of the “X” and the “Y” can equal zero. In such cases, an undefined and zero slope exists, wherein the numerator or the denominator is zero.

## Key Takeaways

- An undefined slope occurs when the line is vertical and has no defined slope value; a zero slope occurs when the line is horizontal and has a slope value of 0.
- An undefined slope is not a finite number and cannot be expressed as a fraction or decimal; a zero slope can be expressed as a fraction with a numerator of 0.
- The undefined slope is perpendicular to the x-axis, while the zero slope is perpendicular to the y-axis.

**Undefined vs. Zero Slope**

A line with a zero slope is a horizontal line that runs parallel to the x-axis. The slope of a horizontal line is always 0 since there is no change in the y-coordinate as the x-coordinate increases. Vertical lines with an undefined slope do not change the x-coordinate as the y-coordinate increases.

**Comparison Table**

Parameter of Comparison | Undefined Slope | Zero Slope |
---|---|---|

Characteristics | The characteristic of an Undefined Slope is a vertical line. | The characteristic of a Zero Slope is a horizontal line. |

Value | An Undefined Slope has a non-existent value since it can not have any concrete value. | A Zero Slope has a value of zero, which is determined. |

Determinants | An Undefined Slope is determined by the variable “X.” | A Zero Slope is determined by the variable “Y.” |

Zero | An Undefined Slope has zero as its denominator. | A Zero Slope has zero as a difference between its numerators. |

Change | The “X” does not change in an Undefined Slope, while the “Y” changes. | In a Zero Slope, the “Y” does not change, whereas the “X” changes. |

**What is an Undefined Slope?**

In simple terms, an Undefined Slope can be defined as a straight line on any graph. It is the slope of a vertical line. The variable “X” does not have an existing value in an Undefined Slope. It is undetermined. The denominator of the Undefined Slope is zero.

Because of this, the value of this slope is non-existent, irrespective of the numerator. The value is always non-existent since any numerator cannot be divided by zero. An “X” variable represents an Undefined Slope.

The difference between the two “X” points is zero. Any line in this slope moves neither to the left nor the right along the “Y” variable. Since there is no change horizontally. The variable “Y” doesn’t change in the case of an Undefined Slope, whereas the variable “X” changes.

**What is Zero Slope?**

Simply put, a Zero Slope is a slope of a horizontal line. A horizontal line on a graph is characterized as a Zero Slope. The “Y” variable represents it. The variable “Y” does not change, whereas the variable “X” keeps changing in the case of a Zero Slope.

The numerator of a Zero Slope is always zero. Thus, the difference between the two points on the “Y” variable is zero. Irrespective of the denominator, the value of the Zero Slope is zero. This makes the slope a determined number.

This is because the numerator is zero; when zero is divided by any number, the result is zero. The Zero Slope is a straight line that does not move upwards or downwards toward the “X” variable. This line runs parallel to the variable “X.”

**Main Differences Between Undefined and Zero Slope**

- In an Undefined Slope, the graph of the line is vertical, whereas on the other hand, in a Zero Slope, the graph of the line is horizontal.
- In an Undefined Slope, the denominator is zero, whereas on the other hand, in a Zero Slope, the difference between the numerators is zero.
- The value of an Undefined Slope is not determined and is non-existent. On the other hand, in the case of a Zero Slope, the value of the slope is determined and is zero.
- The “X” variable represents the Undefined Slope, whereas, on the other hand, the Zero Slope is represented by the variable “Y.”
- An Undefined Slope runs parallel to the “Y” variable, whereas, on the other hand, a Zero Slope runs parallel to the “X” variable.
- In the case of an Undefined Slope, the variable “X” remains constant, whereas the variable “Y” changes. On the other hand, in the case of a Zero Slope, the variable “Y” remains constant, whereas the variable “X” changes.

**References**

- https://link.springer.com/content/pdf/10.1007/s11053-005-6951-3.pdf
- https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB076i008p01905

Last Updated : 11 June, 2023

Emma Smith holds an MA degree in English from Irvine Valley College. She has been a Journalist since 2002, writing articles on the English language, Sports, and Law. Read more about me on her bio page.