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
(yy_{1})=m(xx_{1})
where (x_{1}, y_{1}) 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=(21232)/(1000) = (9/5)
plugging in (0, 32) for (x_{1}, y_{1}) we get
(f32) = (9/5)) * (c0)
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)*f17.77
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=(1000)/(21232) which is 5/9.
Now just plug in either point into the point slope version of the line and get
c=(5/9)*f17.77
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