Maybe I'm just being slow, but:

Why is the slope formula $\displaystyle \frac {\Delta y}{\Delta x} $?

More specifically, why do we divide the change in y by the change in x to get the slope, or incline between two points?

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- Jun 11th 2008, 12:47 PMSkinnerSimple slope question
Maybe I'm just being slow, but:

Why is the slope formula $\displaystyle \frac {\Delta y}{\Delta x} $?

More specifically, why do we divide the change in y by the change in x to get the slope, or incline between two points? - Jun 11th 2008, 01:01 PMTriKri
It can be a very hard question, depending on what you mean. That ratio is basically a quite interesting property of a curve, and has been named slope. You simply want to know how much y increases (or decreases) in proportion to how much x increases. That's as simple.

- Jun 11th 2008, 01:27 PMTKHunny
1) It's a definition. It doesn't have to be any trickier than that.

2) It is a useful definition that provides a basis for comparison. Example:

If I tell you one line increases vertically by 12 and another line increases vertically by 5, what can you say about the two increases? Is one line rising faster than the other?

I await your response. - Jun 11th 2008, 01:29 PMTriKri
For example, you know that the ground level rises 10 meter in a 100 meter (according to the map) long hillside, so the slope is 10/100 = 10 %, which tells you how tough it is to climb if you're out riding a bike.