Question

when the celsius temperature is 30°, the corresponding fahrenheit temperature is 86°. when the celsius temperature is 90°, the corresponding fahrenheit temperature is 194°. 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 f = c?

a. express f as an exact linear function of c.
$f = \frac{9}{5}c + 32$
(simplify your answer. do not include the degree symbol in your answer.)
b. express c as an exact linear function of f.
$c = \square$
(simplify your answer do not include the degree symbol in your answer.)

Explanation:

Step1: Start with the formula from part a

We have \( F = \frac{9}{5}C + 32 \). We need to solve for \( C \). First, subtract 32 from both sides:
\( F - 32=\frac{9}{5}C \)

Step2: Multiply both sides by \( \frac{5}{9} \)

To isolate \( C \), multiply both sides of the equation \( F - 32=\frac{9}{5}C \) by \( \frac{5}{9} \):
\( C=\frac{5}{9}(F - 32) \)
We can also expand this to \( C=\frac{5}{9}F-\frac{160}{9} \), but the factored form is also correct.

Answer:

\( \frac{5}{9}(F - 32) \) (or \( \frac{5}{9}F-\frac{160}{9} \))