Question

You are trying to compare the Fahrenheit and Celsius scales and you have two examples: Temperature A is 50 degrees Celsius and 122 degrees Fahrenheit. Temperature B is 100 degrees Celsius and 212 degrees Fahrenheit. What graph models the relationship between the Fahrenheit and Celsius scales? What is an equation of the line in slope-intercept form?

Answer 1

The graph that models the relationship between the Fahrenheit and Celsius scales is attached below.

An equation of the line in slope-intercept form is F= 9/5 C+ 32.

I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer 2

For this case, the first thing we must do is define variables.
We have then:
c: temperature in degrees celsius
f: temperature in Fahrenheit
The generic equation of the line is:

`f-fo = m (c-co)`
Where, the slope is given by:

`m = (f2-f1)/(c2-c1)`
Substituting values:

`m = (212-122)/(100-50)`
Rewriting:

`m = (90)/(50)`

`m = (9)/(5)`
We choose an ordered pair:

`(co, fo) = (100, 212)` Substituting values in the generic equation:

`f-212 = (9)/(5) (c-100)`
Rewriting:

`f-212 = (9)/(5)c - 180`

`f = (9)/(5)c - 180 + 212`

`f = (9)/(5)c + 32`
Answer:
An equation of the line in slope-intercept form is:

`f = (9)/(5)c + 32`
See attached image.