Physic F.3 ~ Thermometer fast

The length of alcohol column L and the temperature T is assumed to vary linearly, and thus can be represented by a "straight line equation" of the form,

L = aT + b where a and b are constants

At 0'C, L = 3 cm,
thus, 3 = a(0) + b
b = 3 cm

At 50'C, L = 23 cm
thus, 23 = a(50) + 3
a = (23-3)/50 cm/C = 0.4 cm/C

Therefore, at 30'C, L = (0.4 x 30 + 3) cm = 15 cm

(30-0)/(50-0)=(length-3)/(23-3)
3/5*20+3=length
length=15 cm