Question

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? (1). A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius. (2). A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. (3). 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:

If you think of the equation as an equation for a line.

y=mx+by=mx+b

where

C=5/9(F−32)C=5/9(F−32)

or

C=5/9F−5/9(32)C=5/9F−5/9(32)

you can see the slope of the graph is 5/95/9, which means that for an increase of 1 degree Fahrenheit, the increase is 5/95/9 of 1 degree Celsius. Therefore, statement I is true.

This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/59/5 degrees Fahrenheit. Since 9595 = 1.8, statement II is true.

On the other hand, statement III is not true, since a temperature increase of 9/59/5 degrees Fahrenheit, not 5/95/9 degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.

The final answer is D

Step-by-step explanation:

Answer 2

C = 5/9(F - 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. 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. Since 95 = 1.8, statement II is true.

On the other hand, statement III is not true, since a temperature increase of 9/5 degrees Fahrenheit, not 5/9 degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.

The final answer is D.

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