No Slope: An Ambiguous Term

Date: 05/08/2003 at 11:06:00
From: Ashlynne
Subject: The distinction of a line

What is the distinction between a line with a slope of zero and a 
line with no slope?

Date: 05/08/2003 at 12:04:45
From: Doctor Peterson
Subject: Re: The distinction of a line

Hi, Ashlynne.

The phrase "no slope" is ambiguous, and should not be used. In 
everyday English, is means that the line is not sloped, and therefore 
has zero slope (horizontal); but mathematically, it can be argued 
that it means the slope is not defined, which happens when the line 
is vertical. Any ambiguous term is dangerous in math, so it should be 
banned.

The proper terminology is that a horizontal line has zero slope (or 
slope 0), while a vertical line has undefined (or, informally, 
infinite) slope. This is because to find the slope of a vertical line 
you would be dividing by zero, which is not allowed.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/