How is the relation for variation of resistivity with temperature obtained?

The graph of resistivity vs temperature shows a fairly straight line plot over a long range of temperature. Now, let us plot resistivity in the y-axis and temperature in the x-axis.

Now, in my book the relation for variation is given as-

$$\rho-\rho_0=\rho_0\alpha(T-T_0)$$

Now, from the graph one can easily write the equation of a straight line as described above as-

$$\rho-\rho_0=K(T-T_0)$$ for some constant $K$ by using the equation of straight line in slope point form.

Now, my question is what was the necessity to write the constant $K$ as $\rho_0\alpha$. Why did we bother to introduce $\rho_0$ into that term. We generally don't do that while writing equations of straight lines.

• I believe it's because $\rho\propto L$, and just plugging in the formula for thermal expansion – probably_someone Jul 27 '18 at 19:48

$$\frac{\rho-\rho_0}{\rho_0}=\alpha(T-T_0)$$
where $\alpha$ is the constant of proportionality. If you then proposed using $K/\rho_0$ instead, I could ask you the same question: why use a more complex term needlessly?