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. View more lessons or practice this subject at https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:kinetics/x2eef969c74e0d802:concentration-changes-over-time/v/first-order-reactions

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