Question

`=59(F−32)`

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59
A degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

Answer 1

Think of the equation as an equation for a line y = m x + b where in this case C = 5 9 ( F − 32 ) or C = 5 9 F − 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. C = 5 9 ( F ) C = 5 9 ( 1 ) = 5 9 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. C = 5 9 ( F ) 1 = 5 9 ( F ) ( F ) = 9 5 Since 9 5 = 1.8, statement II is true. The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5 9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true: C = 5 9 ( F ) C = 5 9 ( 5 9 ) C = 25 81 ( which is ≠ 1 ) An increase of 5 9 degree Fahrenheit leads to an increase of 25 81 , not 1 degree, Celsius, and so Statement III is not true. The final answer is D.