Question

I really need help in this question I’m not really getting it at all. Thanks so much!

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

Answer: D :)

Explanation:

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=2581(which is ≠ 1)

An increase of 5/9 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D. Hope I helped! :)