Question

When the Celsius temperature is 30degrees​, the corresponding Fahrenheit temperature is 86degrees. When the Celsius temperature is 80degrees​, the corresponding Fahrenheit temperature is 176 degrees . Let C represent the Celsius temperature and F the Fahrenheit temperature.

a. Express F as an exact linear function of C.
b. Solve the equation in part a for​ C, thus expressing C as a function of F.
c. For what temperature is Fequals​C?

Answer 1

First we need to write the general linear function as:

F = a*C + b

Second, we use the 2 first conditions and we have as a equations:

`\left \{ {{86=30a+b} \atop {176=80a+b}} \right.`

Then, resolving the system of equations, we have:

a = 1.8 and b = 32

A) So the linear function is:

F = 1.8*C + 32

B) So in this case we reverse the equation as follow:

`F - 32 = 1.8C\\\\(F-32)/(1.8) = C`

Finally we have:

`C = (F-32)/(1.8)`

C) In this case, we consider F = C and we have:

`C = 1.8C+32\\C = -40`

So

C = F = -40degrees