When the Celsius temperature is 0 degree the corresponding F

When the Celsius temperature is 0 degree, the corresponding Fahrenheit temperature is 32 degree. When the Celsius temperature is 100 degree, the corresponding Fahrenheit temperature is 21 degree. Let C represent the Celsius temperature and F the Fahrenheit temperature. Express F as an exact linear function of C. Solve the equation in part (a) for C, thus expressing C as the function of F. For what temperature is F = C a true statement?

Solution

celsius 0 deg---- 32degF

celsius 100 deg ---- 212degF

slope , m =( 212-32)/ ( 100 - 0) = 180/100 = 1.8 degF/degC

F = mC +k = 1.8C +k , find k bu using one set of point ( 0, 32)

32 = 0 +k ---> k = 32

So,a) F = 1.8C +32

b) Rerranging F and C :

(F -32)/1.8 = C

c) for what temperature is F = C:

from part a) F = 1.8C +32

C = 1.8C +32---> - 0.2C = 32

C = - 160 deg