C=

5

9

(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.