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I only ask this because of the fact that economists tend to plot the dependent variable on the horizontal axis and the independent variable on the vertical, which is opposite to the "normal" way of doing things in math. This leads to the question of how to quantify the slope of a linear function when normally (in basic math) it is

$$\frac{\Delta y}{\Delta x}=\frac{rise}{run}$$

but in economics you'd find the same variables reversed:

$$\frac{\Delta x}{\Delta y}=\frac{run}{rise}$$

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Where are you exactly got stuck? Certainly, you know that the slope means $y'$ at some appropriate points on the curve of $y$. Are you looking for just the differences between two above notations? Indeed, the title, as I am reading it, is different. Thanks. – Babak S. Jul 3 '13 at 15:12
I'm not sure how much you know about economics, but take a supply curve for example - In its most simple form it is a positively sloped linear graph. The price of a certain good is plotted along the vertical axis while the quantity supplied is plotted along the horizontal axis. This creates the reverse of a normal graph in math: A vertical line is a perfectly fine function, but a horizontal line isn't a function. So I'm wondering if the slope of such a graph should be the reverse as well... – agent154 Jul 3 '13 at 15:40
What @agent154 described is more technically called an "inverse" supply curve. When we talk about inverse demand/supply curves, the slope should be d(price)/d(quantity), normally. This is only a convention, without much economic meaning, in my opinion. – Fang Jing Jul 4 '13 at 8:57
up vote 3 down vote accepted

The terms independent/dependent variables are used too loosely in mathematics.

The differentials you listed are simply different ways of looking at something.

Take an economics graph and turn it 90 degrees, 180 degrees..

It will still give you the same information, it's just a different perspective.

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