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 fequalsc?

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:

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:

Finally we have:

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

So

C = F = -40degrees

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )