SOLUTION: PLEASE HELP! ASAP Mrs. Howell, your science teacher, overheard two of her students talking about how to convert temperatures from celsius to farenheit and vice versa. The students

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Question 639286: PLEASE HELP! ASAP Mrs. Howell, your science teacher, overheard two of her students talking about how to convert temperatures from celsius to farenheit and vice versa. The students said they knew there was a formula, but they did not remember what it was it was. Mrs. Howell remarked to you that if they just knew about the freezing point and boiling point of water for each temperature scale, the formula could be easily be "rediscovered." Mrs. Howell has asked you to write a explanation for how to find the formula, showing all of your calculations. Mrs. Howell also wants you to include an explanation of each of the parts of the formula. ( Don't forget to include the formula for celsius to farenheit and the formula for farenheit to celsius.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mrs. Howell remarked to you that if they just knew about the freezing point
and boiling point of water for each temperature scale, the formula could be
easily be "rediscovered."
Mrs. Howell has asked you to write a explanation for how to find the formula,
showing all of your calculations.
Mrs. Howell also wants you to include an explanation of each of the parts of
the formula. ( Don't forget to include the formula for Celsius to Fahrenheit
and the formula for Fahrenheit to Celsius.)
:
we know
Celsius: Water freezes: 0 degrees, Water boils (at sea level): 100 s
Fahrenheit: Water freezes: 32 degrees, Water boils: 212 degrees
:
let x = Fahrenheit degrees
let y = Celsius degrees
:
Using the slope/intercept equation y = mx + b
:
Find the slope, assign the values as follows
x1 = 32; y1 = 0
x2 =212; y2 = 100
m = %28y2-y1%29%2F%28x2-x1%29
m = %28100-0%29%2F%28212-32%29 = 100%2F180 = 5%2F9 is the slope
:
Use the point/slope form to find the equation: y - y1 = m(x-x1)
y -0 = 5%2F9(x - 32)
y = 5%2F9(x-32)
or the familiar formula to convert Fahrenheit to Celsius
c = 5%2F9(f - 32)
:
To convert Celsius to Fahrenheit, solve for f
5%2F9(f - 32) = c
Multiply both sides by 9/5, results:
f - 32 = 9%2F5c
add 32 to both sides
f = 9%2F5c + 32;