Which of the following procedures will allow the student to determine the rate constant, for the reaction?
From the graph it is clear that the reaction follows first order kinetics ($\ce{[X] = [X_0] e^{-kt}}$) where $ [X_0]$ is initial concentration. Taking $ln$ on both sides we get 
$\ce{ln[X] = ln[X_0] +(-kt)}$ 
So if you plot a graph between $ln[X]$ and $t$ then you have the magnitude of slope as k ie the equilibrium constant. 
So correct answer is A.