Light of frequency v falls on material of threshold frequency v_0 ....

When light falls on a metallic surface, ejection of photoelectron results. In this process, conservation of energy holds. Thus, from law of conservation of energy, Energy imparted by the photon = Maximum kinetic energy of the emitted electron + work function of the metal or $\quad h v=(\mathrm{KE})_{\max }+\phi$ but $\phi=h v_0, v_0$ being threshold frequency. $$\begin{array}{ll}\therefore & (\mathrm{KE})_{\max }=h v-h v_0 \\ \text{ or } & (\mathrm{KE})_{\max } \propto v-v_0\end{array}$$