The equation given is:

$C = \frac{5}{9}(F - 32)$

This shows how to convert Fahrenheit (F) to Celsius (C). Let's analyze each statement one by one:

Statement I:

"A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degrees Celsius."

• From the formula, we know that an increase of 1 degree Fahrenheit corresponds to:

$\Delta C = \frac{5}{9} \times \Delta F$

For an increase of 1°F:

$\Delta C = \frac{5}{9} \times 1 = \frac{5}{9} \approx 0.56^\circ C$

So, 1°F increase corresponds to approximately 0.56°C, not 59°C. Statement I is false.

Statement II:

"A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit."

• To convert from Celsius to Fahrenheit, we use the inverse of the conversion formula:

$F = \frac{9}{5}C + 32$

An increase of 1°C corresponds to:

$\Delta F = \frac{9}{5} \times 1 = 1.8^\circ F$

This is correct. Statement II is true.

Statement III:

"A temperature increase of 59 degrees Fahrenheit is equivalent to a temperature increase of 1 degree Celsius."

For an increase of 59°F:

$\Delta C = \frac{5}{9} \times 59 = \frac{295}{9} \approx 32.78^\circ C$

So, an increase of 59°F is approximately 32.78°C, not 1°C. Statement III is false.

Conclusion:

The correct answer is B) II only.

Would you like more details or have any questions about the solution? Here are 5 related questions to explore further:

1. How would you convert a temperature of 100°F to Celsius using the formula?
2. What is the significance of 32°F in the Fahrenheit to Celsius conversion equation?
3. Can you derive the Fahrenheit to Celsius formula from the Celsius to Fahrenheit formula?
4. How does the slope $\frac{5}{9}$ in the equation relate to temperature scales?
5. What