For example, Fahrenheit and Celsius degrees are related in a linear way. Given a table with pairs of both Fahrenheit and Celsius degrees, we can estimate the constants to devise a conversion formula from degrees Fahrenheit to degrees Celsius or vice versa:
⁰F |
⁰C |
5 |
-15 |
14 |
-10 |
23 |
-5 |
32 |
0 |
41 |
5 |
50 |
10 |
Analysis from first principles:
We would like to derive a formula converting F (degrees Fahrenheit) to C (degrees Celsius) as follows:
C=a*F+b
Here, a and b are the constants to be found. A graph of the function C=a*F+b is a straight line and thus is uniquely determined by two points. Therefore, we actually need only the two points from the table, say pairs (F1,C1) and (F2,C2). Then we will have the following:
C1=a*F1+b C2=a*F2+b
Now, C2-C1=(a*F2+b)-(a*F1+b...