Question

Hundred points if solved

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 1

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.