why do they use m for slope in math

Why Is Slope Rise Over Run and Not Run Over Rise? Date: 03/05/2005 at 21:27:04
From: kristin
Subject: Why rise over run??? Someone asked our math teacher yesterday, why is it rise over run and
not run over rise. I was wondering since our teacher didn't know the
answer, if you might. If you could answer this that would be so great!!! I think that maybe it could be both ways bcause like for instance:
(I'm going to show my work here)

(4,2)(3,-7)
2-(-7) / 4-3 = 9/1
y=mx+b
1/9 + 2
y=9/1x + 2

and when you graph it you put the dot at the 2 place and go up 9
lines and go out one line and put a dot (then connect those dots)
BUT you can also put a dot at the 2 go out one, and up 9 and put a
dot there (then connect) and it's the same thing. Do you think rise
over run can also be run over rise??? Date: 03/05/2005 at 23:04:40
From: Doctor Peterson
Subject: Re: Why rise over run???


Hi, Kristin. There are at least two questions here: why do we define the word
slope to mean the ratio of rise to run, and why is that the
right number to use in the slope-intercept form of a line? The answer to the first question is that any number we assign to a
slope ought to be bigger when the line is sloped more steeply. We
want the slope to tell us how much the line is sloped. A steeper
line goes up more in the same distance:

o
/
/
/ o
/ /
/ /
o o
steep less steep

If we used the run over the rise, then the less steep line would
have a greater slope, which wouldn't make sense:

o
/
/
/ o
/ /
/ /
o-----+ o-----+
6/6 3/6 -- actual slope: steeper has greater slope
6/6 6/3 -- run/rise: steeper has smaller slope!


How about the question of what goes in the m spot in the equation? Let's look at the intercept and one other point on the line:

/
o (x,y)
/
/
(0,b) o-----+


+---------------

What is the slope of that line? y-b y-b
m = --- = ---
x-0 x

If we multiply both sides of the equation by x, we get

mx = y - b

and adding b to both sides gives

mx + b = y

So if we define slope as rise/run, then this is the equation that any
point on the line has to fit. If you defined slope differently, you
would get a different equation. So here's how it works: we define slope in a way that makes sense
based on what the word slope means; then we find that we can use
that slope value in an equation that describes any point on the line. One could use a different formula for something like slope, and get
a different equation; but this one gives us a reasonable definition
AND a nice little equation to use it in.


If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum
http://mathforum. org/dr. math/
One guess as to why БMБ is used for slope has to do with the French word for climb, Бmonter;Б another explanation is because both mountains and movement begin with the letter БM. Б If БMБ is derived from the French word for climbing, that would be ironic, because the French do not use БMБ to denote slope in an equation; rather they use БAБ for slope, perhaps because of "ascending" or "Alps," though that is not known for certain either. Slope is also sometimes called Бmodulus of slope,Б which begins with the letter БM. Б

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