Calculus Word Problem

Question

The graph of Celsius temperature, C, as a function of Fahrenheit temperature, F, is a line. It is known that 0 degrees C and 32 degrees F both represent the temperature at which water freezes. Similarly, 100 degrees C and 212 degrees F both represent water’s boiling point. Write the mathematical formula of the function C = f(F).

Answer 1

Well if y is F and x is C then the function goes through (0,32) and (100,212)

It's a line so

y = mx + b

When x = 0, y = 32, so b = 32

y = mx + 32

Slope of the line is (212-32) / (100 - 0) = 1.8

m = 1.8

so y = 1.8x + 32

F = 1.8C + 32