HELP

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
(Is it D I need to know if this is right to see if I am on the right track)

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
9
F−
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
(whichis≠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.

Answer 2

thank you so much (@sally? earthworm sally), with your explanation I fully understand whats going on.

Answer 3

Weird!! Sally and i am dumb are the same person.

Did you enjoy talking to yourself?

Answer 4

Now if you really want to know what is going on here whatever names the one of you are then start with freezing and boiling of water.
water freezes at 0 C and 32 F
water boils at 100 C and 212 F
find a line that fits those points in the forn
C = m F + b
0 = m(32) + b
100 = m(212 )+ b
so
100 = m(212-32)
100 = 180 m
m = 10/18 = 5/9 remarkable
then
0 = (5/9) (32) + b
b = - (5/9)(32)
so in the end
C = (5/9)(F-32)

now the slope m 5/9 is the change in C / change in F
and
9/5 is therefore the change in F/change in C