Why is temperature coefficient divided by reference resistance?
If we used your scheme, \$ R_{t} = mt + R_{0} \$ then we would need a unique m for every resistance value. This would be a pain.

A more useful parameter is the temperature coefficient expressed as a percentage or factor. So, given a temperature coefficient of resistance of 0.2%/K and, say, a &Delta;T of 12&deg;C then I know that a 1k resistor will increase by \$ 1k \cdot 0.002 \cdot 12 \$ and 47 &Omega; resistor will increase by the same ratio or \$ 47 \cdot 0.002 \cdot 12 \$.

The big advantage is that the one parameter can be applied to all the resistors in a catalogue series.

I would write the formula as

$$ \alpha = \frac {R_{T1} - R_{T0}}{R_{T0} (T_1 - T_0)} $$

where \$ R_{T0} \$ is the reference resistance at temperature \$ T_0 \$, \$ R_{T1} \$ is the resistance at temperature \$ T_1 \$ and \$ \alpha \$ is the temperature coefficient.