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If a graph is plotted between temperature of a body on degree Celsius (along y-axis) and degree Fahrenheit [along x-axis] at different temperatures, then the slope of the graph will be:
- a)5/9
- b)9/5
- c)3/5
- d)5/3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If a graph is plotted between temperature of a body on degree Celsius...
To understand why the slope of the graph between Celsius and Fahrenheit temperatures is 5/9, we need to consider the relationship between these two temperature scales.
1. Understanding the Celsius and Fahrenheit Scales:
- The Celsius scale is based on the freezing and boiling points of water. The freezing point of water is 0 degrees Celsius (°C), and the boiling point is 100°C.
- The Fahrenheit scale is also based on the freezing and boiling points of water. However, the freezing point is 32 degrees Fahrenheit (°F), and the boiling point is 212°F.
2. Converting Between Celsius and Fahrenheit:
- To convert from Celsius to Fahrenheit, we use the following formula:
°F = (9/5) × °C + 32
This formula scales the Celsius temperature by 9/5 and adds 32 to obtain the corresponding Fahrenheit temperature.
- To convert from Fahrenheit to Celsius, we use the following formula:
°C = (°F - 32) × (5/9)
This formula subtracts 32 from the Fahrenheit temperature and scales the result by 5/9 to obtain the Celsius temperature.
3. Relationship between Celsius and Fahrenheit Temperature Scales:
- We can observe that the relationship between the Celsius and Fahrenheit scales is linear.
- For any given temperature point, if we increase the Celsius temperature by 1 degree, the corresponding Fahrenheit temperature will increase by 9/5 or 1.8 degrees.
- This linear relationship is reflected in the slope of the graph between Celsius and Fahrenheit temperatures.
4. Slope of the Graph:
- The slope of a linear graph represents the rate of change between the variables on the x-axis and y-axis.
- In this case, the x-axis represents the Fahrenheit temperature and the y-axis represents the Celsius temperature.
- Since the relationship between Celsius and Fahrenheit temperatures is linear, the slope of the graph is constant.
5. Calculating the Slope:
- To calculate the slope, we can choose any two points on the graph and find the change in y (Celsius) divided by the change in x (Fahrenheit).
- Let's consider two points on the graph: (0°F, 0°C) and (1°F, 5/9°C).
- The change in y is 5/9°C, and the change in x is 1°F.
- Therefore, the slope is (5/9°C) / (1°F) = 5/9.
Therefore, the slope of the graph between Celsius and Fahrenheit temperatures is 5/9.
1. Understanding the Celsius and Fahrenheit Scales:
- The Celsius scale is based on the freezing and boiling points of water. The freezing point of water is 0 degrees Celsius (°C), and the boiling point is 100°C.
- The Fahrenheit scale is also based on the freezing and boiling points of water. However, the freezing point is 32 degrees Fahrenheit (°F), and the boiling point is 212°F.
2. Converting Between Celsius and Fahrenheit:
- To convert from Celsius to Fahrenheit, we use the following formula:
°F = (9/5) × °C + 32
This formula scales the Celsius temperature by 9/5 and adds 32 to obtain the corresponding Fahrenheit temperature.
- To convert from Fahrenheit to Celsius, we use the following formula:
°C = (°F - 32) × (5/9)
This formula subtracts 32 from the Fahrenheit temperature and scales the result by 5/9 to obtain the Celsius temperature.
3. Relationship between Celsius and Fahrenheit Temperature Scales:
- We can observe that the relationship between the Celsius and Fahrenheit scales is linear.
- For any given temperature point, if we increase the Celsius temperature by 1 degree, the corresponding Fahrenheit temperature will increase by 9/5 or 1.8 degrees.
- This linear relationship is reflected in the slope of the graph between Celsius and Fahrenheit temperatures.
4. Slope of the Graph:
- The slope of a linear graph represents the rate of change between the variables on the x-axis and y-axis.
- In this case, the x-axis represents the Fahrenheit temperature and the y-axis represents the Celsius temperature.
- Since the relationship between Celsius and Fahrenheit temperatures is linear, the slope of the graph is constant.
5. Calculating the Slope:
- To calculate the slope, we can choose any two points on the graph and find the change in y (Celsius) divided by the change in x (Fahrenheit).
- Let's consider two points on the graph: (0°F, 0°C) and (1°F, 5/9°C).
- The change in y is 5/9°C, and the change in x is 1°F.
- Therefore, the slope is (5/9°C) / (1°F) = 5/9.
Therefore, the slope of the graph between Celsius and Fahrenheit temperatures is 5/9.
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Community Answer
If a graph is plotted between temperature of a body on degree Celsius...
The relation between degree celsius and degree Fahrenheit is,
C - along y-axis
F - along x-axis
y = mx+c .. equation of straight line
On comparing we get,
Slope = m = 5/9.
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