Question

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

Q. How temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation C= 5/9 (F−32)?

1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 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 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

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D. I and II Only

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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° Fahrenheit, the increase is 5/9 of 1° 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° Celsius is equal to an increase of 95° Fahrenheit.

⇒C = 5/9(F)

⇒1 = 5/9(F)

⇒(F) = 9/5

Since 9/5 = 1.8

So, Statement II is true.

59 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° Celsius

So, Statement III is not true.

The only answer that has both statement I and statement II as true is D.

Answer 2

Correct Question

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equatio 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 ✔✔

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Answer is in the attachment