https://file.aiquickdraw.com/mathbot/file/1726339230579j14j5k16.jpg

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

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? I: A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degrees Celsius. II: A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. III: A temperature increase of 59 degrees Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

Learn how to solve a temperature conversion problem involving Fahrenheit and Celsius. This problem explores key algebraic concepts, including the formulas for converting between Fahrenheit and Celsius. Suitable for students in Grades 9-12.

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