The relationship between temperature measured on the Celsius

The relationship between temperature measured on the Celsius scale and on the Fahrenheit scale is linear. The freezing point of water is 0°C and 32°F, and the boiling point is 100°C and 212°F.

(a) Find an equation giving the relationship between the temperature F measured on the Fahrenheit scale and the temperature C measured on the Celsius scale.
F =  

(b) Find F as a function of C, and use this formula to determine the temperature in Fahrenheit corresponding to a temperature of 30°C. (Round your answer to one decimal place.)
°F

(c) Find C as a function of F, and use this formula to determine the temperature in Celsius corresponding to a temperature of 90°F. (Round your answer to one decimal place.)
°C

Solution

a)

F = b0 + b1 C

As

b1 = (212 - 32) / (100 - 0) = 1.8

Then

F = b0 + 1.8C

Using C=0, F = 32,

32 = b0 + 1.8*0

b0 = 32

Thusm

F = 32 + 1.8C [ANSWER]

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b)

F = 32 + 1.8C [ANSWER]

If C = 30,

F = 32+1.8*30 = 86 [ANSWER]

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c)

Solving for C in terms of F,

C = (F-32)/1.8 [ANSWER]

Thus, if F = 90,

C = (90-32)/1.8 = 32.2 [ANSWER]