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Difference Between Undefined and Zero Slope

Undefined vs Zero Slope

Slope, in mathematics, is the rise or run between two points on a given line. Slope also measures the “steepness” of the line. The slope consists of two pair of points or coordinates that are represented by variables in form of letters “X” and “Y.” Any change in variable “Y” will affect the “X” variable.

The slope, lines, and points are plotted on a chart with integers (both positive and negative) on both the “X” and “Y” axis. The zero is placed in the center of the graph and lies in the intersection of both the “Y” and “X” axis. The system used to denote where the lines are drawn is the Cartesian system. The slope is often used in mathematical word problems especially linear equations.

Slopes are used in many different areas that include economics, architecture and construction, trend analysis and interpretation in social, health, and market situations. Anything that requires a scale and a graph has a use for measuring the slope. Also, in everyday life, a slope is also everywhere. Anything that includes steepness or an angle in everyday objects or observation can be measured by using the formula for the slope.

The formula for finding the slope is “M” (standing for the slope) that is equal to the quotient of (Y2 – Y1) over (X1 – X2). In this situation, the “Y” variables represent the numerator, and the same goes for the “X” variables which represent the denominator. Usually, the slope is often expressed as positive or negative (variables are often integers). However, there are instances that the variables in both “X” and “Y” coordinates can equal to the value of zero. In these situations, an undefined and zero slope occurs when either the numerator or denominator equals zero.

In a zero slope, the numerator is zero. This means that the “Y” points (Y1 and Y2) produce a difference of zero between the variables. Zero divided by any non-zero denominator will result in zero. This also results in a straight, horizontal line on the graph that neither climbs nor descends along the “X” axis. Between the two points, “Y” is not changing but “X” is increasing. The line is drawn as parallel to the “X” axis. Even though the slope is zero, it is still a determined number compared to the undefined slope.

An undefined slope is characterized by a straight, vertical line on the graph with the “X” coordinate points having no existing value of slope. In this situation, the difference between the two “X” points equals to zero. The “X” coordinate, being the denominator, will yield an undefined answer despite the value of the numerator. It is a rule that anything decided by zero is an undefined value since nothing can be divided by zero. The line in the undefined slope doesn’t move to the left or the right along the “Y” axis.

Graphing and drawing the slope, whether zero, undefined, positive or negative involves two points and a line. Some people attach arrowheads to the line to indicate the direction of the line. The points on the coordinates should be blackened to point out the intersections of both variables.


1.An undefined slope is characterized by a vertical line while a zero slope has a horizontal line.
2.The undefined slope has a zero as the denominator while the zero slope has a difference of zero as a numerator.
3.The zero slope has a determined value (which is zero) while the undefined slope cannot have a concrete value which makes the value non-existent.
4.The zero slope is determined by the “Y” variables (as a difference between the variables) while the undefined slope is determined in the same way by the “X” variable.

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