How to work this problem

Question

Construct a formula that relates the temperature of a given object in degrees Fahrenheit to that of the temperature
in degrees Celsius. Be sure to define each variable. Finally, compute the temperature, from your given equation, at
which a temperature in degrees Fahrenheit is equal to that in degrees Celsius.

Answer 1

Let C = the temperature in Celsius

      F = the temperature in Fahrenheit

 

The boiling point of water at sea level is 100 °C or 212 °F.

The freezing point of water at sea level is 0 °C or 32 °F.

 

To relate degrees Fahrenheit to degrees Celsius, C is the independent variable and F is the dependent variable, F=f(C).

We have two points,  (0,32) and (100,212)   [note: these are (F,C)]

 

We may use the two-point formula for the equation of a line:

    y - y₁ = (y₂-y₁)/(x₂-x₁)x - x₁

 

   C - 32 = (212-32)/(100-0)F - 0

   C - 32 = (180/100)F

     C = (9/5)F + 32

 

When are they equal?    (when does C=F ?; set either to equal the other

   F = (9/5)F + 32

   5F = 9F + 160             [multiply by 5 to get rid of fraction]

   -4F = 160                    [subtract 9F from both sids]

      F = -40

  When F=-40, C=-40

 

Check:

   C = (9/5)F + 32

   -40 = (9/5)(-40) + 32   ?

   -40 = -72 + 32   ?

   -40 = -40   ?yes

Answer 2

I always remember 2 different temperatures

0 Celsius = 32 fahrenheit (freezing pt of water)

100 Celsius = 212 Fahrenheit (boiling pt of water)

 

with this you can calculate equation since it is a linear function.

let y = Celsius and X = Fahrenheit.

y = ax+b

our slope is a which is change in y over X = (100-0)/(212-32)=100/180=5/9

 

to get b plug in a pt say (32,0)

0=5/9*32+b which means b = -5/9*32.

 

so we have

y=5/9(X-32)

 

to to find when same let y=X=C

so

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

get c together

4/9C = -5/9*32

C = -40.

 

thus -40 Fahrenheit equals -40 Celsius.

hope helpful. best - David