Question:
Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?
Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?
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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.
Updated On: Mar 25, 2026
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The Correct Option is A
Approach Solution - 1
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).
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Approach Solution -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:
\[ \boxed{\text{The figure represents the relation between Celsius and Fahrenheit temperatures.}}\]
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:
\[ \boxed{\text{The figure represents the relation between Celsius and Fahrenheit temperatures.}}\]
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