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In the slope equation,the increase of x is divided to the increase of y.But I cannot understand,why we cannot use the increase of y is divide to the increase of x.Everyone said,the gradient of the tangent to the curve at a point is one over one,increase in y divided by increase in x,etc....But they cannot tell why the increase of Y divide by increase of X and why we cannot use the increase of x divided by increase of y.

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    $\begingroup$ Yes, that would give as much information as "change in y divided by change in x". But we need to choose one way or the other to have a specific function and chose to use "change in y divided by change in x". One reason for that choice is that we tend to think (though it is not mathematically required) of the function y= f(x) as "a value of x causes a change in y". A change in x causes a change in y. "Change in y divided by change in x" answers "how much change in y is caused by change in x?"\cdot\cdot\cdot$ $\endgroup$
    – user247327
    Apr 10 '17 at 18:27
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Consider a constant function, for example. You would say that the slope equals zero in that case. For an arbitrary increase in x, the increase of y would be zero, so x/y would not be defined. It doesn't make sense that way considering that the slope is meant to increase when the increase of y is bigger along a constant difference in x.

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