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 = (y2 – y1) / (x2 – x1)
But, in our case, we are using “F” and “C”… So,
m = (C2 – C1) / (F2 – F1)
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!