Caculate
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?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius. II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III. A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
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1 solution
ANSWER 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=5/9F − 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(which is ≠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 I and II only.