When the Celsius temperature is 10 degrees, the corresponding Fahrenheit temperature is 50 degrees...

Question

When the Celsius temperature is 10 degrees, the corresponding Fahrenheit temperature is 50 degrees. When the Celsius temperature is 115 degrees, the corresponding Fahrenheit temperature is 239 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 F=C?

 

Answer 1

(a)

 

Use equation of type y = mx + b:  F = mC + b

 

m = (F2 - F1) / (C2 - C1) = (239 - 50) / (115 - 10) = 1.8

 

F = 1.8C + b

 

50 = 1.8(10) + b

 

b = 32

 

F = 1.8C + 32 = (9/5)C + 32

 

(b)

 

C = (5/9)(F - 32)

 

(c)

 

 

C = 1.8C + 32

 

C = -40