Saturday, November 16, 2013

Celsius and Fahrenheit

Question:  The table below contains information on the boiling point and freezing point of water in both Celsius and Fahrenheit.  The relationship between the two temperature measures is linear.  Write a linear equation where the temperature in fahrenheit is a function of the temperature in celsius.  Write a linear equation where the temperature in Celsius is a function of the temperate in Fahrenheit. 


Celsius Fahrenheit
Boiling Point
100
212
Freezing Point
0
32


Answer:  The standard point slope form of a line can be written as 

(y-y1)=m(x-x1

where (x1, y1) is any point,

m is the slope of the line.

When x=c (where c is the temperature in celsius) and y=f is the temperature in fahrenheit, the slope m is

m=(212-32)/(100-0) = (9/5)

plugging in (0, 32) for (x1, y1) we get

(f-32) = (9/5)) * (c-0)

or

f=(9/5)*c + 32

Now we can rearrange this equation to solve for c as a function of f.

c=(5/9)*f- (5/9)*32

which is 

c=(5/9)*f-17.77

Let’s check this equation by plugging f=212 into it.  (We had better get c=100)

We do!!!!

Happy Happy Joy Joy !!!!!


Another way to get the answer for c as a function of f is to get the point slope equation for a line where x is f and y is c.

The slope in this case is m=(100-0)/(212-32) which is 5/9.

Now just plug in either point into the point slope version of the line and get 

c=(5/9)*f-17.77











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