Question

Find the linear function C = f(F) that gives the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that C=0 when F=32 (freezing point) and C=100 when F=212 (boiling point).

Answer 1

The linear function C = f(F) that relates the Celsius and Fahrenheit temperature scales is C = (5/9)(F - 32).

Step-by-step explanation:

To find the linear function C = f(F) that relates the Celsius and Fahrenheit temperature scales, we can use the facts that C=0 when F=32 (freezing point) and C=100 when F=212 (boiling point).

We can start by finding the slope of the linear function. The slope, represented by 'm', is calculated as (change in Celsius temperature)/(change in Fahrenheit temperature).

In this case, the change in Celsius temperature is 100-0 = 100, and the change in Fahrenheit temperature is 212-32 = 180. Therefore, the slope 'm' is 100/180 = 5/9.

Using the point-slope form of a linear function, we have C - 0 = (5/9)(F - 32), which simplifies to C = (5/9)(F - 32).

Learn more about temperature conversion