The celcius scale is devised so that 0 degrees celcius is the freezing point of water ( at 1 atmosphere of pressure) and 100 degrees celcius is the boiling point of water ( at 1 atmosphere of pressure) . If you are more familiar with the Fahrenheit scale, then you know that water freezes at 32 degrees fahrenheit and boils at 212 degrees fahrenheit. Find a linear equation that relates temperature measured in degrees celcius and temperature measured in degrees fahrenheit.
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To find the linear equation that relates temperature measured in degrees Celsius (C) and temperature measured in degrees Fahrenheit (F), we can use the relationship between freezing and boiling points of water in both scales.
Let's consider the freezing point of water. We know that at this point, in degrees Celsius, the temperature is 0°C, and in degrees Fahrenheit, the temperature is 32°F. We can use this information to form one point on our line: (0, 32).
Next, let's consider the boiling point of water. At this point, in degrees Celsius, the temperature is 100°C, and in degrees Fahrenheit, the temperature is 212°F. This gives us another point on our line: (100, 212).
We have two points: (0, 32) and (100, 212). Now we can find the equation of the line using the formula for the slope-intercept form of a line, y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's find the slope by using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) = (0, 32) and (x2, y2) = (100, 212).
m = (212 - 32) / (100 - 0)
m = 180 / 100
m = 9/5
Now that we have the slope, we can use one of the points (0, 32) to find the y-intercept (b).
Using the slope-intercept form of the line, we have:
y = mx + b
Substitute the values for (x, y) = (0, 32) and m = 9/5:
32 = (9/5)(0) + b
32 = 0 + b
b = 32
Therefore, the y-intercept is 32.
Now we can write the equation of the line in slope-intercept form:
F = (9/5)C + 32
So the linear equation that relates temperature measured in degrees Celsius (C) and temperature measured in degrees Fahrenheit (F) is:
F = (9/5)C + 32
To find a linear equation that relates temperature measured in degrees Celsius (C) and temperature measured in degrees Fahrenheit (F), we can use the relationship between the two scales at two specific points.
Let's consider the freezing point of water, which is 0 degrees Celsius (C) and 32 degrees Fahrenheit (F).
Using the formula relating Celsius and Fahrenheit conversions:
F = (9/5)C + 32
Substituting C = 0 and F = 32:
32 = (9/5)(0) + 32
32 = 32
This verifies that at the freezing point of water, the equation holds.
Now, let's consider the boiling point of water, which is 100 degrees Celsius (C) and 212 degrees Fahrenheit (F).
Again using the conversion formula:
F = (9/5)C + 32
Substituting C = 100 and F = 212:
212 = (9/5)(100) + 32
212 = 180 + 32
212 = 212
This verifies that at the boiling point of water, the equation also holds.
So, based on these two points, we can say that the linear equation that relates temperature measured in degrees Celsius (C) and temperature measured in degrees Fahrenheit (F) is:
F = (9/5)C + 32