Question

The equation above shows how temperature F,measured in degrees Fahrenheit,Relates to temperature C,measured in degrees Celsius.Based on the equation,Which of the follow must be true?

Answer 1

Check the complete question attached. 

We have the equation $C= \frac{5}{9} (F-31)$ equation (1); solving for F we get: 
$\frac{9}{5} C=F-31$
$F= \frac{9}{5} C+31$
$F= \frac{9}{5} (C+31)$ equation (2)

I. To check this we are going to use equation (1) to see what hapen when temperature rises from 32 Fahrenheit  to 33 Fahrenheit:
For 32 Fahrenheit:
$C= \frac{5}{9} (32-31)$
$C= \frac{5}{9} (1)$
$C= \frac{5}{9}$ 

For 33 Fahrenheit:
$C= \frac{5}{9} (33-31)$
$C= \frac{5}{9} (2)$
$C= \frac{10}{9}$ 
Now we are going to subtract the two temperatures in degrees Celsius:
$\frac{10}{9} - \frac{5}{9} = \frac{5}{9}$ As you can see, the temperature increased $\frac{5}{9}$ degree Celsius.  

We can conclude that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius. 

II. To check this one we are going to use equation (2) to see what happens when temperature raises from 1 degree Celsius to 2 degrees Celsius:
For 1 degree Celsius:
$F= \frac{9}{5} (C+31)$
$F= \frac{9}{5} (1+31)$
$F= \frac{9}{5} (32)$
$F=57.6$

For 2 degrees Celsius:
$F= \frac{9}{5} (C+31)$
$F= \frac{9}{5} (2+31)$
$F= \frac{9}{5} (33)$
$F=59.4$
Now we are going to subtract the two temperatures in Fahrenheit: 
$59.4-57.6=1.8$ As you can see, the temperature increased 1.8 Fahrenheit. 

We can conclude that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8  Fahrenheit.

III. Since a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius, we can conclude that this one is false. 

The correct answer is D) I and II only