Find the linear function cequalsf(f) that gives the reading on the celsius temperature scale corresponding to a reading on the fahrenheit scale. use the facts that cequals0 when fequals32 (freezing point) and cequals100 when fequals212 (boiling point). b. at what temperature are the celsius and fahrenheit readings equal?

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

They both read equal at Z = - 40

Explanation:

We are looking for a linear function so we can write the following condition

Y = aX + b

Applying it to the exercise we got C = a F + b

Let's use the facts that C = 0 when F = 32 and C = 100 when F = 212

0 = 32 a + b            (1)

100 = 212 a + b       (2)

From (1) b = - 32 a , when we replace this in (2) we obtain a = (5/9)

and b = - (5/9)32 = - 160/9

Finally the linear function is C = (5/9) F - (160/9)

Both readings are equal at a Z number so

Z = (5/9) Z - 160/9

(4/9) Z = -160/9 and Z = - 40