When the Celsius temperature is [tex]35^\circ[/tex], the corresponding Fahrenheit temperature is [tex]95^\circ[/tex]. When the Celsius temperature is [tex]115^\circ[/tex], the corresponding Fahrenheit temperature is [tex]239^\circ[/tex]. Let [tex]C[/tex] represent the Celsius temperature and [tex]F[/tex] the Fahrenheit temperature.

a. Express [tex]F[/tex] as an exact linear function of [tex]C[/tex].

b. Solve the equation in part a for [tex]C[/tex], thus expressing [tex]C[/tex] as a function of [tex]F[/tex].

c. For what temperature is [tex]F = C[/tex]?

The Fahrenheit temperature (F) can be expressed as an exact linear function of the Celsius temperature (C) using the formula: F = (9/5)C + 32. To express C as a function of F, we can rearrange the formula as: C = (5/9)(F - 32). For F = C, the temperature is -40 degrees.

Explanation:

To express Fahrenheit (F) as an exact linear function of Celsius (C), we can use the formula for converting Celsius to Fahrenheit: F = (9/5)C + 32.

To solve for C in terms of F, we can rearrange the formula as: C = (5/9)(F - 32).

Now, let's find the temperature at which F = C:

Setting the two equations equal to each other:

(9/5)C + 32 = C

Subtracting C from both sides:

(9/5)C - C = -32

Combining like terms:

(4/5)C = -32

Multiplying both sides by 5/4:

C = -32 * (5/4)

Simplifying:

C = -40

Therefore, for F = C, the temperature is -40 degrees.

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