Question

Write a linear equation that expresses the relationship between the temperature in degrees Celsius (C) and degrees Fahrenheit (F). Use the fact that water freezes at 0°C (32°F) and boils at 100°C (212°F).

Answer 1

Answer:

$\displaystyle F=\frac{9}{5}C+32$

$\displaystyle C=\frac{5}{9}(F-32)$

Explanation:

Temperature Units Conversion

The conversion formula between Celsius and Fahrenheit temperature scales is well-known. But we'll use the provided data to derive the formula. Let's model the relationship between Fahrenheit (F) and Celsius (C) as a linear function like

$F=mC+b$

Where m and b must be computed according to the pair of conditions given. The values for each temperature scale are (C,F)=(0,32) and (100,212). Replacing the first value

$32=m\times 0+b$

It means that  

$b=32$

By using the second point

$212=m\times 100+32$

Solving for m

$\displaystyle m=\frac{212-32}{100}=\frac{180}{100}$

Simplifying

$\displaystyle m=\frac{9}{5}$

So, the conversion formula is

$\displaystyle F=\frac{9}{5}C+32$

Which is the widely known formula for temperature conversion

Solving for C, we get the inverse relation

$\boxed{\displaystyle C=\frac{5}{9}(F-32)}$