Question

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

• A.
• B.
• C.
• D.

Hint:

Remember that the relation between Celsius and Fahrenheit is linear, but it does not pass through the origin. The conversion factor is \( \frac{9}{5} \), and the y-intercept is 32.

Answer 1

The Correct Option is A

The relation between Celsius and Fahrenheit temperatures is given by the linear equation: \[ F = \frac{9}{5}C + 32. \] This is a straight line with a slope of \( \frac{9}{5} \) and a y-intercept of 32, meaning that when the Celsius temperature is 0°C, the Fahrenheit temperature is 32°F. Thus, the relationship between Celsius and Fahrenheit is a straight line with a positive slope that does not pass through the origin but intersects the Fahrenheit axis at 32°F. In the provided options, the correct figure is one where the line passes through the origin and has a positive slope, matching the relationship of the Celsius to Fahrenheit scale (but offset by the starting point). 
Final Answer: Option (1).

Answer 2

Step 1: Understand the temperature conversion relation.
The relation between Celsius and Fahrenheit temperatures is linear. The formula for converting Celsius temperature (\( C \)) to Fahrenheit temperature (\( F \)) is: \[ F = \frac{9}{5}C + 32. \] This equation represents a straight line with a slope of \( \frac{9}{5} \) and a y-intercept of 32.

Step 2: Analyze the figure.
The figure provided shows a straight line passing through the origin (0, 0) and decreasing in a linear fashion. This suggests that it is a representation of a temperature scale with a negative slope, which is consistent with the equation \( F = \frac{9}{5}C + 32 \), where the y-intercept corresponds to 32 degrees (the freezing point of water in Fahrenheit).

Step 3: Conclusion.
The figure represents the correct relationship between Celsius and Fahrenheit temperatures.

Final Answer:
\[ \boxed{\text{The figure represents the relation between Celsius and Fahrenheit temperatures.}}\]