The integrated rate law for the first-order reaction A -> _products_ is ln[A]_ _t_ = - _kt_ \+ ln[A]_0. Because this equation has the form _y_ = _mx_ \+ _b_ , a plot of the natural log of [A] as a function of time yields a straight line. The rate constant for the reaction can be determined from the slope of the line, which is equal to - _k_.
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