Let                   t = ax + b
So that            80 = ax_i+ b
400 = ax_s+ b

Which gives, a=\frac{320}{x_s-x_i}, b=80-320\left[\frac{x_i}{x_s-x_i}\right]

t^{\circ} M =320\left[\frac{x-x_i}{x_s-x_i}\right]+80

Also, t^{\circ} C =100\left[\frac{x-x_i}{x_s-x_i}\right]

\therefore t°M = 3.2 t°C + 80

Now \frac{T_s}{T_i}=1.366

And T_s-T_i=400-80=320

\begin{aligned}&T_i=\frac{320}{0.366}=874.3^{\circ} N \\\\&T_s=1194.3^{\circ} N\end{aligned}

T°N abs = (t°N – 80) + 874.3 = t°N + 794.3

At t°N = 0°N, we get

T°N abs = 0°N + 794.3 = 794.3