Before we explain undefined vs zero slope, it’s necessary to know some background info.

Math can be seen as a way of representing and making sense of the world through numbers and representation. It’s a logical and analytical subject.

Anything and everything around us can be represented with the help of mathematics. Like what shape is the water bottle one carries in their backpack, or what is the volume of the backpack itself.

Theoretical physics is highly dependent on math, theoretical physicists prove or predict phenomena. Therefore, math is everywhere from calculating daily expenses to predicting the existence of white holes in space.

There are different branches of math like algebra, arithmetic, trigonometry, geometry, statistics. Graph theory is also a sub-brunch of mathematics.

In a simple way, graph theory is all about a set of dots or points connected by a line joining them. Graph theory is all about studying those dots or nodes, as they are called, and analyzing what the relation between the nodes signifies.

It is a way of studying data. There are two axes ( usually x and y) against which these points are plotted. Every node is an intersection point of two values against each of the axis. The point where the x and the y axis meet has the coefficient of (0,0) and from there it goes on. This is how graphs work.

The difference between **undefined slope and zero slopes** is that for each of them, the coefficient value of either x or y is zero. For undefined slope, zero is the denominator and for zero slopes, zero is the numerator.

## Comparison Table: Undefined vs Zero Slope

Criteria | Undefined Slope | Zero Slope |
---|---|---|

Definition | An undefined slope is a vertical slope whose denominator is always zero. | Zero slope is a horizontal slope on a graph paper whose numerator is always zero. |

Value | The undefined slope is called an undefined slope because its value is undefined. The denominator in the case of an undefined slope is zero and anything divided by zero cannot have a value. | The value of a zero slope is zero because the value is zero divided by anything is zero. This is why it is called a zero slope. |

Determinant | One of the easy ways to determine an undefined slope or zero slope is to look for the constant value between the two coefficients. Therefore, an undefined slope is determined by the coefficient of x. | Zero slope is determined by the coefficient value of y. |

Parallel | The undefined slope is a vertical line and as such, it is parallel to the y axis. | Zero slope is a horizontal line and as such, it is parallel to the x-axis. |

Change | In an undefined slope, the x remains constant while y changes. | In a zero slope, y remains co stand while x changes. |

## About Undefined Slope

A slope is mathematically defined as rise over run. In simpler terms, it is the change of co-efficient of y against the coefficient of x.

All the available coefficients of x and y are plotted and they are joined by a line and that is called the slope. The horizontal axis is usually the x-axis and the vertical axis is the y axis.

The formula for finding the slope is the quotient of **(y2-y1) over (x2-x1)**. The undefined slope is a vertical line because there is no change in the coefficient of x.

This makes the denominator zero which makes the slope undefined. It is because anything divided by zero gives an undefined answer because nothing can be divided by zero. The line obtained in an undefined slope doesn’t move to the right or left of the y axis.

In other words, the run of the slope is zero. A quick way to identify an undefined slope is to check if both the coordinates of x are the same, then the slope would be undefined.

A good example of an undefined slope is an elevator, which goes only up and down.

## About Zero Slope

Slopes are usually known to be positive, negative, and undefined but slopes in a linear equation can also be zero. What happens when the numerator in the equation for the slope becomes zero, the is the difference between the two coefficients of y comes as zero.

The zero slope is neither positive nor negative. The zero slope is a horizontal slope as opposed to the vertical one of the undefined slope.

This slope remains parallel to the x-axis. The zero slope is represented by the y variable. The y variable here doesn’t change whereas the x variable keeps changing which is in contrast with the undefined slope.

Just like the undefined slope doesn’t move left or right of the y axis, the zero slope doesn’t move upwards or downwards towards the x-axis.

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## Difference Between Undefined Slope and Zero Slope

### Definition

Both undefined slop and zero slope are slopes obtained by plotting coefficients of x and y on a graph paper against the x and y-axis. The undefined slope is a vertical slope whose denominator is always zero.

Zero slope is a horizontal slope on a graph paper whose numerator is always zero.

### Value

The undefined slope is called an undefined slope because its value is undefined. The denominator in the case of an undefined slope is zero and anything divided by zero cannot have a value.

The value of a zero slope is zero because the value is zero divided by anything is zero. This is why it is called a zero slope.

### Determinant

One of the easy ways to determine the undefined slope or zero slope is to look for the constant value between the two coefficients. Therefore, an undefined slope is determined by the coefficient of x. Zero slope is determined by the coefficient value of y.

### Parallel

An Undefined slope is a vertical line and as such, it is parallel to the y axis. Zero slope is a horizontal line and as such, it is parallel to the x-axis.

### Change

In an undefined slope, the x remains constant while y changes. In a zero slope, y remains co stand while x changes.

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