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Take any two points whose x coordinates are different.Suppose they are P = (Xp, Yp) and Q = (Xq, Yq)
then slope = (Yp - Yq)/(Xp - Xq) = (Yq - Yp)/(Xq - Xp), that is the change in the y coordinate between the two points ("rise") divided by the change in the x coordinate between the points - taken in the same order ("run").
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For a straight line, you calculate delta-y divided by delta-x (in other words, difference in y-coordinates, divided by difference in x-coordinates), for two different pointsFor an arbitrary curve, you calculate the derivative. This basically means that you analyze what happens if you choose two points that get closer and closer together.
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