\[ C = \frac{5}{9}(F  32)\]
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?
A. I 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. The final answer is D.
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