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Wow Sujan, great thinking.
If you have a curve, THEN slope of the curve at a given point is the derivative. But, if you have a linear line, then slope of that line is simply (Y2  Y1) / (X2  X1). (no need of derivative)
And coming back to Elasticity, it is ((X2  X1)/X1) / ((Y2  Y1)/Y1)
So, you see, there is difference in equations for Slope and Elasticity.

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