\[ C = \frac{5}{9}(F - 32)\]

The above equation shows the relationship between Celcius (C) and Fahrenheit (F), both a measure of temperature. Based on this equation, which of the following must be true?

temperature increase of 5/9 degree Celcius. II. A temperature increase of 1 degree Celcius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celcius. |

A. I Only.

B. II Only.

C. III Only.

D. I and II Only.

B. II Only.

C. III Only.

D. I and II Only.

**Answer:**

The above equation shows a linear relationship between two variables, C and F. Hence, we can think of it as

**y=mx+b**, where

\[ C = \frac{5}{9}(F - 32)\]

or

\[ C = \frac{5}{9}F - \frac{5}{9}(32)\]

you can see the slope of the graph is 5/9, which means that for an increase of 1 degree Fahrenheit, the increase is 5/9 of 1 degree Celsius. Therefore, statement I is true.

This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5 degrees Fahrenheit. Since 9/5 = 1.8, statement II is true.

On the other hand, statement III is not true, since a temperature increase of 9/5 degrees Fahrenheit, and not 5/9 degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.

This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5 degrees Fahrenheit. Since 9/5 = 1.8, statement II is true.

On the other hand, statement III is not true, since a temperature increase of 9/5 degrees Fahrenheit, and not 5/9 degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.

**The final answer is D.**