Question

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.


​

Answer 1

$\mathfrak{\huge{\blue{\underline{\underline{AnswEr :}}}}}$

D. I and II Only

$\mathfrak{\huge{\blue{\underline{\underline{ExplanaTion :}}}}}$

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

hey mate...

here is your answer...

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

95 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

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 degree, Celsius, and so Statement III is not true.

The final answer is D.

hope it helps...