Question

Need answer with explanations:

C=59(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 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 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

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Think of the equation as an equation for a line

y=mx+b

where in this case

C=59(F−32)

or

C=59F−59(32)

You can see the slope of the graph is 59, which means that for an increase of 1 degree Fahrenheit, the increase is 59 of 1 degree Celsius.

C=59(F)

C=59(1)=59

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 95 degrees Fahrenheit.

C=59(F)

1=59(F)

(F)=95

Since 95 = 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 59 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

C=59(F)

C=59(59)

C=2581(whichis≠1)

An increase of 59 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.
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Answer 2

$<b>$

Think of the equation as an equation for a line y=mx+b where in this case C=59(F−32) or C=59F−59(32) You can see the slope of the graph is 59, which means that for an increase of 1 degree Fahrenheit, the increase is 59 of 1 degree Celsius. C=59(F) C=59(1)=59 Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 95 degrees Fahrenheit. C=59(F) 1=59(F) (F)=95

Since 95 = 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 59 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true: C=59(F) C=59(59) C=2581(whichis≠1) An increase of 59 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true