The steam point and the ice point of a mercury thermometer are marked as 80° and 10°. At what temperature on centigrade scale will the reading of this thermometer be 59°C ?

Let the relation between the thermometer reading and centigrade scale be y = ax + b.
Given, at x = 100, y = 80 and at x = 0, y = 10
$\therefore$                        80 = 100a + b, 10 = b $\Rightarrow$ a = 0.7
Now, we have to find x when y = 59
                            59 = 0.7x + 10 $\Rightarrow$ x = 70
$\therefore$ At 70° C, the reading of given thermometer be 59°C.