Types of Slopes of a Line

Generally, there are three (3) types of slopes of a line, namely positive, negative, and zero slopes. The fourth one is a bit controversial.

  1. Positive Slope
  2. Negative Slope
  3. Zero Slope
  4. Undefined Slope (also known as Infinite Slope)

Note: The fourth on the list is not considered a type of slope because this is the case of a vertical line where the line is parallel to the y-axis, and it does not have a movement along the x-axis. In other words, a vertical line goes up and down; therefore, it does not have a steepness at all.

This is also referred to as the undefined slope because the denominator is zero. Remember the concept of slope as the rise over run. The rise (numerator) describes the change in \large{y} which is written symbolically as \color{blue}\Delta \,y. Meanwhile, the run (denominator) describes the change in \large{x} which is written as \color{red}\Delta \,x.

In the case of the Undefined Slope, the value of the numerator or \color{blue}\Delta \,y is a nonzero integer while the denominator or \color{red}\Delta \,x is equal to \large{0}. Thus, we have:

how an undefined slope looks like

Check out how Mr. Piggy can help us remember the concepts of the different kinds of slopes of a straight line.


Positive Slope

A positive slope means the line is increasing when viewed from left to right.

As you can see, Mr. Piggy is having a hard time going up since it costs him an extra effort for an uphill climb.

positive slope

Negative Slope

A negative slope means the line is decreasing when viewed from left to right.

Thanks to gravity, Mr. Piggy is definitely enjoying the slide because it takes him less effort to go down.

negative slope

Zero Slope

A zero slope means the line is neither increasing nor decreasing when viewed from left to right, or vice versa. Simply put, the slope of a horizontal line is zero, \large0.

Mr. Piggy is free to showcase his running skills on this level ground.

zero slope

Undefined Slope or Infinite Slope

An undefined slope or infinite slope, means the line is neither moving to the left nor to the right such as the case of a vertical line. The slope of a vertical line is either + \,\infty or - \,\infty .

In this situation, Mr. Piggy will experience the endless “fall” of his lifetime!

undefined slope

You might be interested in:

Slope Formula

Slope-Intercept Form of a Line

Point-Slope Form of a Line