College Algebra

Question

Water freezes at 0 degrees Celsius, which is the same as 32 degrees Fahrenheit. Also water boils at 100 degrees Celsius, which is the same as 212 degrees Fahrenheit. (Use fractions in your answers.)
(a) Use the freezing and boiling points of water to find a formula expressing Celsius temperature C as a linear function of the Fahrenheit temperature F.
C =


(b) What is the slope of the function you found in part (a)?



Explain its meaning in practical terms.
This means that for every one degree increase in the Fahrenheit temperature, the Celsius temperature will increase by
degrees.

Answer 1

Hello, thank you for taking the time to post your question!

The general form in slope-intercept form for this expression is C = mF + b , where “m” is the slope and “b” is the y-intercept.

I would start by computing the slope from the two points given

m = (100 – 0) / (212 – 32) = 100 / 180 = 5/9

then the y-intercept is

0 = 32(5/9) + b

0 = 160/9 + b

b = -160/9

so the full equation here is C = 5/9F – 160/9, with a slope of 5/9. That means that for every one-degree increase in the Fahrenheit temperature, the Celsius temperature will increase by 5/9 degree

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

 

 I do this with my algebra classes all the time.

 

 

 (32,0) and (212,100)

 

 the slope is (100-0)/(212-32) = 100/180 = 5/9

 

 intercept B = y - mx = 0 - (5/9)(32) = 0 - 160/9 = -160/9

 

the line equation is y = 5/9 x + -160/9 = 5/9 x - 160/9

 

                                                          = 5/9 (x - 32)

 

changing the vars, let x=F and y=C.

              C = 5/9(F-32)

 

so 1 degree celsius is 5/9 degree Fahrenheit

Hence 1 degree fahrenheit is 9/5 degree celsius

 

solving for F.....

(9/5)C = F - 32

 

F = (9/5)C+32