In a first order reaction, reactant concentration 'C' varies with time 't' as

For first order reaction,$\frac{\mathrm{k}\cdot \mathrm{t}}{2.303}=\log \left[{\mathrm{C}}_0\right]-\log \left[\mathrm{C}\right]$
or,              $\log \left[\mathrm{C}\right]=\log \left[{\mathrm{C}}_0\right]-\frac{\mathrm{k}\cdot \mathrm{t}}{2.303}$
$\therefore$Plot of log [C] vs t is a straight with negative slope.