Question 639286
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 = {{{(y2-y1)/(x2-x1)}}}
m = {{{(100-0)/(212-32)}}} = {{{100/180}}} = {{{5/9}}} is the slope
:
Use the point/slope form to find the equation: y - y1 = m(x-x1)
y -0 = {{{5/9}}}(x - 32)
y = {{{5/9}}}(x-32)
or the familiar formula to convert Fahrenheit to Celsius
c = {{{5/9}}}(f - 32)
:
To convert Celsius to Fahrenheit, solve for f
{{{5/9}}}(f - 32) = c
Multiply both sides by 9/5, results:
f - 32 = {{{9/5}}}c
add 32 to both sides
f = {{{9/5}}}c + 32;