**Q: How can I make up an equation that will convert Fahrenheit to Celsius (or vice versa)??**

A: Converting Fahrenheit to Celsius is a linear process. What does that mean? The equation is a “y = mx + b” type… So,

C = mF + b

(C = Celsius and F = Fahrenheit)…. I could also do F = mC + b… But, I am going to stick with the first method I picked.

Now, I need a few data points… Things that I know about Fahrenheit and Celsius…. I know that

32 Fahrenheit = 0 Celsius [freezing point]

and that

212 Fahrenheit = 100 Celsius [boiling point]

So, I have the data points (32, 0) and (212, 100) to use in my equation:

C = mF + b

How do I calculate the slope (m)? Use our regular slope equation:

m = (y_{2} – y_{1}) / (x_{2} – x_{1})

But, in our case, we are using “F” and “C”… So,

m = (C_{2} – C_{1}) / (F_{2} – F_{1})

m = (100 – 0) / (212 – 32)

m = 100 / 180

m = 5 / 9

So, we know that:

C = mF + b

C = (5/9)F + b

Now, plug in a point to solve for b. I will use the point (32, 0):

0 = (5/9)(32) + b

0 = 160/9 + b

-160/9 = b

So,

**C = (5/9)F – 160/9**

For example, let’s say you were given 15 degrees Fahrenheit and asked to convert it to Celsius: Simply plug in 15 for F:

**C = (5/9)(15) – 160/9 and solve!**

OR, let’s say you were given 20 degrees Celsius and asked to convert it to Fahrenheit: Simply plug in 20 for C:

**20 = (5/9)F – 160/9 and solve!
**