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).

Respuesta :

Answer:

[tex]\displaystyle F=\frac{9}{5}C+32[/tex]

[tex]\displaystyle C=\frac{5}{9}(F-32)[/tex]

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

[tex]F=mC+b[/tex]

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

[tex]32=m\times 0+b[/tex]

It means that  

[tex]b=32[/tex]

By using the second point

[tex]212=m\times 100+32[/tex]

Solving for m

[tex]\displaystyle m=\frac{212-32}{100}=\frac{180}{100}[/tex]

Simplifying

[tex]\displaystyle m=\frac{9}{5}[/tex]

So, the conversion formula is

[tex]\displaystyle F=\frac{9}{5}C+32[/tex]

Which is the widely known formula for temperature conversion

Solving for C, we get the inverse relation

[tex]\boxed{\displaystyle C=\frac{5}{9}(F-32)}[/tex]

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