Question

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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 $\huge \: \frac{5}{9}$ 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 $\huge \: \frac{5}{9}$ 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

$\huge \mathcal \red{Answer:-}$

Think of the equation as an equation for a line

Y = MX + B

where in this case

$\huge \: C= \frac{5}{9} (F−32)$

or

$\huge \: C= \frac{5}{9} \: F− \frac{5}{9} (32)$

You can see the slope of the graph is $\huge \: \frac{5}{9}$ , which means that for an increase of 1 degree Fahrenheit, the increase is $\huge \: \frac{5}{9}$ of 1 degree Celsius.

$\huge \: C= \frac{5}{9} (F)$

$\huge \: C= \frac{5}{9}(1) = \frac{5}{9}$

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of $\huge \: \frac{5}{9}$ degrees Fahrenheit

$\huge \: C= \frac{5}{9} (F)$

$\huge \: C= \frac{5}{9} (F)$

$\huge \: 1= \frac{5}{9} (F)$

$\huge \: (F)= \frac{5}{9}$

Since $\huge \: \frac{5}{9}$ = 1.8, statement 2 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 $\huge \: \frac{5}{9}$ degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

$\huge \: C= \frac{5}{9} (F)$

$\huge \: C= \frac{5}{9} ( \frac{5}{9} )$

The final answer is D.

Answer 2

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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 $\huge \: \frac{5}{9}$ 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 $\huge \: \frac{5}{9}$ 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