$\ln \left(\frac{T_f-T_0}{T-T_0}\right)=K t$

If $\theta$ is the instantaneous temperature than

$\ln \left(\frac{\theta_i-\theta_0}{\theta-\theta_0}\right)=K t$

$\ln \left(\theta_i-\theta_0\right)-\ln \left(\theta-\theta_0\right)=K T$    $\left\{\begin{array}{l}\theta_i \longrightarrow \text { initial temperature } \\ \theta_0 \longrightarrow \text { temperature of surrounding }\end{array}\right\}$

$\ln \left(\theta-\theta_0\right)=-K t+\ln \left(\theta_i-\theta_0\right)$

Comparing to

$y=m x+C$