Undefined Slope and Zero Slope

Date: 04/11/97 at 12:31:39
From: Shelia V. Atkins
Subject: Undefined Slope and Zero Slope

What is the difference between an undefined slope and a slope of zero?
I have read my book, and I can't seem to find the answer anywhere.

Date: 04/11/97 at 13:59:34
From: Doctor Mike
Subject: Re: Undefined Slope and Zero Slope

Dear Shelia,
  
Yes, this is a subtle difference.  Here is the straight info.
  
A horizontal line has a slope which is the number zero.  You might be 
familiar with the standard "slope/intercept" form of the equation of a 
line y = mx+b where m stands for the slope. If you use zero for m you 
just get y = b which is the standard form for a horizontal line.  
  
A vertical line does not have a slope.  It's not a question of not 
knowing what the slope is equal to; it doesn't exist.  There isn't 
one.  That is what is meant by saying it has "undefined" slope.  
  
Here's another way to look at it.  If you take a horizontal line and 
tilt it more and more so it gets closer and closer to being vertical 
(straight up and down) but not actually vertical, then the slope of 
the line gets bigger and bigger.  If a line is just one degree away 
from being vertical then its slope is about 57. If a line is only 1/10 
of a degree away from being vertical, then its slope is about 573.  
You could even have a line which is *almost* vertical with a slope 
of one billion!  Following this trend, the slope of a vertical line 
would have to be infinity, but infinity is not a real number, so we 
just have to say that the idea of slope is not defined or doesn't make 
sense for a vertical line.

I hope this helps.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/