Question

John is going on a trip and the country he is traveling to uses the Celsius scale. He is curious about converting Celsius temperatures to Fahrenheit. John determines 68°F is equivalent to 20°C and 86°F is equivalent to 30°C.

Which function models the relationship between Fahrenheit and Celsius?

Answer 1

The answer is 9/5c + 32

Answer 2

`f(x)=(9)/(5)x+32` converts Celsius to Fahrenheit.

`g(x)=(5(x-32))/(9)` converts Fahrenheit to Celsius.

Explanation:

Write given data in the table

`\begin{array}{cc}x&f(x)\\^(\circ)\text{C}&^(\circ)\text{F}\\20&68\\30&86\end{array}`

Let the expression for the function be

`f(x)=ax+b`

Note, that this equation is linear equation and it is well-known fact that the Celsius to Fahrenheit dependence is linear.

Substitute corresponding values into this expression:

`68=20a+b\\ \\86=30a+b`

Subtract these two equations:

`86-68=30a-20a\\ \\10a=18\\ \\a=(9)/(5)`

Substitute it into the first equation:

`68=20\cdot (9)/(5)+b\Rightarrow b=68-36=32`

So,

`f(x)=(9)/(5)x+32`

This is the function which converts Celsius to Fahrenheit.

And function

`g(x)=(5(x-32))/(9)` converts Fahrenheit to Celsius.