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April 11th, 2017, 03:28 PM   #1
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Why do we do y1-y2 x1-x2

Was wondering why we don't do the opposite x1-×2 y1-y2? Or does it not matter? Would it lead to undefined answers when they wouldn't be over wise?

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Last edited by skipjack; April 12th, 2017 at 05:47 AM.
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April 11th, 2017, 03:42 PM   #2
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wat?
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April 11th, 2017, 03:45 PM   #3
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2 * 3 = 6 ....hang on...and..and..and 3 * 2 = 6 !!!!!!!!!!
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April 11th, 2017, 05:41 PM   #4
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Quote:
Why do we do y1-y2 x1-x2
is that an attempt to write the formula for slope?

$m = \dfrac{y_1-y_2}{x_1-x_2}$

the standard definition for slope is $\dfrac{\Delta y}{\Delta x}$ ... that's why.
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April 11th, 2017, 09:16 PM   #5
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$\dfrac{y_1-y_2}{x_1-x_2}$ and $\dfrac{y_2-y_1}{x_2-x_1}$ are equivalent. Their reciprocals give the slope of $x$ with respect to $y$.
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Last edited by skipjack; April 12th, 2017 at 05:44 AM.
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April 12th, 2017, 01:28 AM   #6
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If you calculated $\displaystyle \frac{x_2 - x_1}{y_2 - y_1}$, you'd just calculate something different... If you wanted some sort of measure which increases the more horizontal a line or curve is (i.e. instead of "steepness" you want "shallowness"... a bigger number means a more shallow line/curve) then I suppose $\displaystyle \frac{x_2 - x_1}{y_2 - y_1}$ could be useful. Otherwise, I wouldn't bother with it.
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April 12th, 2017, 09:41 AM   #7
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It is conventional to show y as the dependent variable and x as the independent variable. That is why the conventional notation is y = some formula in x. It is frequently important that we know how the dependent variable (conventionally y) will change in response to a change in the independent variable (conventionally x).

Now we could measure the ratio between the change in y and the change in x as

$\dfrac{\Delta x}{\Delta y}$ or $\dfrac{\Delta y}{\Delta x}$ where $\Delta$ means change in.

It is convenient to measure the ratio as $\dfrac{\Delta y}{\Delta x}$ because that gives a simpler formula for linear equations, namely

$y = b + \dfrac{\Delta y}{\Delta x}$ instead of

$y = b + \dfrac{x}{\dfrac{\Delta x}{\Delta y}}.$

Everyone prefers to multiply than to divide. So the convention is

$\dfrac{\Delta y}{\Delta x}.$
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April 12th, 2017, 12:44 PM   #8
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Quote:
Originally Posted by JeffM1 View Post
It is conventional to show y as the dependent variable and x as the independent variable. That is why the conventional notation is y = some formula in x. It is frequently important that we know how the dependent variable (conventionally y) will change in response to a change in the independent variable (conventionally x).

Now we could measure the ratio between the change in y and the change in x as

$\dfrac{\Delta x}{\Delta y}$ or $\dfrac{\Delta y}{\Delta x}$ where $\Delta$ means change in.

It is convenient to measure the ratio as $\dfrac{\Delta y}{\Delta x}$ because that gives a simpler formula for linear equations, namely

$y = b + \dfrac{\Delta y}{\Delta x}$ instead of

$y = b + \dfrac{x}{\dfrac{\Delta x}{\Delta y}}.$

Everyone prefers to multiply than to divide. So the convention is

$\dfrac{\Delta y}{\Delta x}.$
okay, thanks everyone. it just seemed to help me do it left to right.
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