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-
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.