(a) If the temperature changes 1° Fahrenheit, how many degrees does the Celsius temperature change? [Hint: See Exercise 1.]
(b) What happens to the Fahrenheit temperature when the Celsius temperature changes 1°?
(c) How are your answers in parts (a) and (b) related to the formulas in Exercises 1?
Exercises 1
The Fahrenheit and Celsius scales for measuring temperatures are linearly related. They are calibrated using the freezing and boiling points of water at sea level.
Temperature Scale | Fahrenheit Scale | Celsius Scale |
Water Freezes | 32° | 0° |
Water Boils | 212° | 100° |
(a) Use the data in the table to write a formula that relates the Fahrenheit temperature F to the Celsius temperature C. Your answer should be in the form F = mC + b.
(b) Solve the equation in part (a) for C to find a formula that relates the Celsius temperature to the Fahrenheit temperature.
(c) When is the temperature in degrees Fahrenheit the same as the temperature in degrees Celsius?
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