Writing a Linear Equation

Question

Temperature measured in degrees Celsius (C) is related to temperature measured in degrees Fahrenheit (F) by a linear equation. Water boils at 100°C and 212°F. Water freezes at 0°C and 32°F. Find the linear equation relating Celsius and Fahrenheit temperatures. 

Answer 1

There are specific equations for converting temperatures from Fahrenheit to Celsius and Celsius to Fahrenheit. To change a temperature in Celsius to Fahrenheit, you multiply the temperature by 9/5 and then add 32. Written as an equation, this would be 9/5 x C + 32.

To convert a temperature from Fahrenheit to Celsius, you subtract 32 from the Fahrenheit temperature, then multiple by 5/9, or (F - 32) x 5/9.

To prove this, you can use the boiling point of water as an example. In Celsius, water boils at 100 degrees and in Fahrenheit it boils at 212 degrees. If you use the C to F (Celsius to Fahrenheit) equation, your problem would look like this: 9/5 x 100 + 32. When you multiply a fraction by a whole number, you multiply the numerator (the top number) of the fraction - in this case, 9 - by the whole number, then divide that number by the denominator (the bottom number). So 9/5 x 100 = (9 x 100)/5 = 900/5 = 180. So, 9/5 x C + 32 = 180 + 32 = 212.

To go from F to C (Fahrenheit to Celsius), use the second equation, which would look like this: (212 - 32) x 5/9 = 180 x 5/9 = (180 x 5)/9 = 900/9 = 100. Therefore, both equations are proven.