Math Help - Why Does m Represent the Slope of the Line

1. Why Does m Represent the Slope of the Line

Why Does m Represent the slope of the line?

I use s for slope. My equation is y = sx + b.

I could also use I for Intercept.

The equation can be expressed y = sx + I. What is wrong with that?

Does anyone know a link explaining why m has been used to represent slope?

What do you think about my equation representing the y-intercept?

2. Re: Why Does m Represent the Slope of the Line

Originally Posted by nycmath
Why Does m Represent the slope of the line?
I use s for slope. My equation is y = sx + b.
I could also use I for Intercept.
The equation can be expressed y = sx + I. What is wrong with that?
Not a thing is wrong with it.

m & b are accidents of history. But you will have impossible task in trying to change tradition.

3. Re: Why Does m Represent the Slope of the Line

"Dr. Math", http://mathforum.org/dr.math/faq/faq.terms.html,gives a number of possible derivations, beginning with the fact that "monter" is French for "climb", but say that we really don't know.

4. Re: Why Does m Represent the Slope of the Line

You can use whatever symbols you want as the constants for slope and itrecept, as long as you define them for the reader. Same thing with variables x and y - there is absolutely no rule that you have to use 'x' for the independent variable and 'y' for the dependent variable. However we're all so used to using them this way that it makes iot easy to understand the equation y = mx + b. Changing things makes it harder to understand - for example you are free to define m as the independent variable, x as the slope, y as the y-intercept and b as the dependent variable and write b = xm + y, which is legal but would cause a world of confusion.

I once had an economics professor who used the greek letter $\phi$ for everthing - he would use $\phi$ for price in one lecture, $\phi$ for demand in another, and $\phi$ for quantity in yet another. If he needed to differentiate between them he threw in some "prime" symbols. My notes would have really curious equations like $\phi' = \phi'' \phi + \phi'''$. Perfectly correct but not helpful at all.

5. Re: Why Does m Represent the Slope of the Line

This reminds me a story about Serge Lang from here (PDF). I may have seen it on this forum recently.

"While on sabbatical at Harvard, he sat in on a course Mazur was giving and often criticized the notation. Eventually they decided to give him a T-shirt which said, “This notation sucks” on it. So one day Barry intentionally tried to get him to say it. He introduced a complex variable Ξ, took its complex conjugate, and divided by the original Ξ. This was written as a vertical fraction, so it looked like eight horizontal lines on the blackboard. He then did a few other similar things, but Serge kept quiet—apparently he didn’t criticize notation unless he knew what the underlying mathematics was about. Eventually Barry had to give up and just present him with the T-shirt."

6. Re: Why Does m Represent the Slope of the Line

Thank you everyone. I truly appreciate every feedback.

7. Re: Why Does m Represent the Slope of the Line

Originally Posted by HallsofIvy
"Dr. Math", http://mathforum.org/dr.math/faq/faq.terms.html,gives a number of possible derivations, beginning with the fact that "monter" is French for "climb", but say that we really don't know.
That's funny cause in France they usually use "y = ax + b"!!!