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Convert temperature from Celsius to Fahrenheit

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?
I found the formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. It gave me the following data points:
Fahrenheit Celsius
Freezing point of water 32 0
Boiling point of water 212 100
Could you please help me :
1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.
2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.
3. How do the graphs of these two functions differ? choose a value of x and generate the associated f(x).
Do not just list the functions. I need to show all of the steps which were used to derive the functions.

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Let call degree Fahrenheit F
and degree Celsius C

We assume that F is a linear function of C, hence it has the form F=a*C + b
Substitute the above temperatures into this equation:
At the ...

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