SOLUTION: The boiling point of water is 373 K, or 212 degrees F. The freezing point of water is 273 K or 32 degrees F. The relationship between Kelvin and Fahrenheit temperatures is linear.

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Question 954208: The boiling point of water is 373 K, or 212 degrees F. The freezing point of water is 273 K or 32 degrees F. The relationship between Kelvin and Fahrenheit temperatures is linear.
a) write a linear function expressing K(F) in terms of F.
b) find the inverse of the function in part (a). What does it mean?
c) A normal human body temperature is 98.6 degrees F. What is the corresponding Kelvin temperature?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You have two data points, (F,K). They are (212,373) and (32,273).

K as a function of F:
K=%28%28373-273%29%2F%28212-32%29%29F%2Bb in slope-intercept form.
b=K-mF
Pick a point...
b=273-%28%28373-273%29%2F%28212-32%29%29%2A32

Evaluate b, substitute it into the first equation for K and simplify.
m=10%2F18=5%2F9
-
b=273-%285%2F9%29%2A32
b=255.2

highlight%28K=%285%2F9%29F%2B255.2%29

Inverse?
y=%285%2F9%29F%2B255
switch: F=%285%2F9%29y%2B255
F-255=%285%2F9%29y
%28F-255%29%289%2F5%29=y
y is the inverse of K.
y=K%5E-1=%289%2F5%29F-255%2A%289%2F5%29
highlight%28y=K%5E%28-1%29=%289%2F5%29F-459.4%29, but unsure of the practical meaning.