Question

The boiling point of water is 212 oF or 100 oC. The freezing pointis 32 oF or 0 oC. If the equation relating oF, to oC is of the form oF = aoC + b, find a and b.

Answer 1

The equation relating temperature in Fahrenheit to temperature in Celsius is given by °F = 9/5°C + 32. The boiling and freezing points of water can be used as known data points to determine the values of a and b in the equation.

Step-by-step explanation:

The equation relating temperature in Fahrenheit (°F) to temperature in Celsius (°C) is given by: °F = a°C + b. To determine the values of a and b, we can use two known data points - the boiling point and freezing point of water. By substituting the values of 212°F and 100°C for °F and °C respectively, we can solve for a and b.

Solution

At the boiling point of water, °F = 212 and °C = 100. Substituting these values into the equation gives: 212 = 100a + b.

1. At the freezing point of water, °F = 32 and °C = 0. Substituting these values into the equation gives: 32 = 0a + b.
2. Solving this system of equations simultaneously, we find that a = 9/5 and b = 32.

Therefore, the equation relating °F to °C is °F = 9/5°C + 32.

Learn more about Temperature conversion