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? 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

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 5/9degree Fahrenheit leads to an increase of 25/81, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.

Hope that helped!!

Answer 2

The equation

`C=(5)/(9)(F-32)`

tells us that the slope is 5/9. By definition, this means that if you increase F by one, C will increase by 5/9.

Inversely, the slope would become 9/5=1.8. This means that if you increase C by one, F will increase by 1.8.