## 207. Math Puzzle $8 / 82$

In a thermometer, the indication (length of the mercury column) is a linear function of the temperature. Peter has an intact thermometer tube and wants to create a scale for it. He measures a length of $15 \mathrm{~cm}$ at $20^{\circ} \mathrm{C}$ and $10 \mathrm{~cm}$ at $10^{\circ} \mathrm{C}$. How should he proceed when drawing the scale?
For a thermometer, the length of the mercury column $y$ is a linear function of the temperature $x$.

Thus, the approach is: $15=20 a+b, 10=10 a+b$, from which $a=0.5, b=5$.

The zero point of the thermometer scale is at a length of $50 \mathrm{~m}$ from the reference point, the scale interval is $0.5 \mathrm{~cm} / \mathrm{K}\left(1 \mathrm{~K}=1^{\circ}\right.$ temperature difference $)$.