C=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
5
9
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 EXPLANATION: Think of the equation as an equation for a line

y=mx+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
(whichis≠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.