The integrated rate law for a first-order reaction is expressed as: \[ \log[A] = \log[A]_0 - \frac{k}{2.303} t \] This equation aligns with the linear form \( y = c - mt \). In this context, the slope \( m \) is \( \frac{k}{2.303} \). The negative sign signifies a reduction in concentration over time. Consequently, the slope of the plot of \(\log[A]\) against time is: \[ -\frac{k}{2.303} \]