# For a first order reaction $A\rightarrow 2B$ ,graph for $\large\frac{d[B]}{dt}$ vs $\large\frac{-d[A]}{dt}$ is

Given $A\rightarrow 2B \rightarrow -\large\frac{d[A]}{dt}=\frac{1}{2}\frac{d[B]}{dt}$
In this case the y-axis is $\large \frac{d[B]}{dt}$ and the x-axis is $-\large\frac{d[A]}{dt}$, so this is a line in the form of $y -2x =0$. Graph (D) is the right graph that represents this among the four choices.
edited Jul 26, 2014