Find the linear function c equals=f(f) that gives the reading on the celsius temperature scale corresponding to a reading on the fahrenheit scale. use the facts that equals=0 when fequals=32 (freezing point) and cequals=100 when fequals=212 (boiling point). b. at what temperature are the celsius and fahrenheit readings equal

a. C(F) = (5/9).F - (160/9)

b. They both readings are equal at C = F = - 40

Explanation:

They are telling us that we are looking for a linear function

If C(F) = a.F + b is the linear function, we use the data to find a and b

C(32) = a.32 + b

0 = a.32 + b

b = - (a.32)     (1)

And then

C(212) = a.212 + b

100 = a.212 + b    (2)

replacing (1) in (2) we obtain

100 = a.212 +  [-(a.32)]

100 = a.212 - a.32

100 = 180.a

a = 100/180

a = 5/9

If a = 5/9 then b = -(a.32)

b = - (5/9).32

b = - (160/9) and the linear function is

C(F) = (5/9).F - (160/9)

For b. they are asking us for a X reading. We must equalize C and F

X = (5/9).X - (160/9)

(4/9).X = - (160/9)

X = -40

C = F at temperature X = - 40