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]