Question

The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the linear relationship between C and F

Answer 1

Choose Celsius degree along the x-axis and Fahrenheit degree along the y-axis.

Given a Freezing point in Celsius = 0°C

The freezing point in Fahrenheit degree = 32°F

∴ The Freezing point is (0°, 32°)

Also given Boiling point in Celsius = 100°C

The boiling point in Fahrenheit = 212°F

∴ The Boding point is (100°, 212°)

Let C denote the Celsius degree and F denote the Fahrenheit degree.

The equation of the path connecting the freezing point (0°, 32°) and the boiling point (100°, 212°) is

`("C" - 0)/(100 - 0) = ("F" - 32)/(212 - 32)`

`"C"/100 = ("F" - 32)/180`

`"C"/5 = ("F" - 32)/9`

C = `5/9("F" - 32)`  .......(1)

Which is the required relation connecting C and F.