We know that 32 degrees Fahrenheit is equivalent to 0 degrees Celsius and that 212 degrees Fahrenheit is equivalent to 100 degrees Celsius. Use the trend curve to determine the relationship between Fahrenheit and Celsius temperatures. When you create your initial chart, before clicking Finish, you must indicate that data is in columns and not rows because with only two data points, Excel assumes different variables are in different rows.
The Correct Answer and Explanation is :
To determine the relationship between Fahrenheit (°F) and Celsius (°C) temperatures, we can use the known data points of 32°F = 0°C and 212°F = 100°C to establish a linear equation. The relationship between Fahrenheit and Celsius is linear because the temperature conversion follows a constant rate of change.
Step 1: Identify the formula
The general formula for converting Fahrenheit to Celsius is: C=59(F−32)C = \frac{5}{9}(F – 32)
Where:
- CC is the temperature in Celsius.
- FF is the temperature in Fahrenheit.
This formula comes from the linear equation between the two scales. The slope of the line (mm) represents the rate of change, and the y-intercept (bb) is the point where the line crosses the Celsius axis when F=0F = 0.
Step 2: Derive the formula from two points
The two given data points are:
- (32°F, 0°C)
- (212°F, 100°C)
Using the point-slope formula for a straight line: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}
Substitute the given points: m=100−0212−32=100180=59m = \frac{100 – 0}{212 – 32} = \frac{100}{180} = \frac{5}{9}
Thus, the slope of the line is 59\frac{5}{9}, confirming that the relationship between Fahrenheit and Celsius is linear.
Step 3: Interpret the equation
The slope (59\frac{5}{9}) tells us that for every 9 degrees Fahrenheit, the Celsius temperature changes by 5 degrees. The formula can now be written as: C=59(F−32)C = \frac{5}{9}(F – 32)
This equation shows how to convert Fahrenheit temperatures into Celsius.
Step 4: Set up the Excel chart
To create a chart in Excel:
- Enter the data points (32°F, 0°C) and (212°F, 100°C) in columns. Excel assumes different variables are in rows by default, so ensure that your data for Fahrenheit and Celsius is organized in columns (not rows) to avoid incorrect assumptions by Excel.
- Plot the data points on the graph and apply the trendline to represent the linear relationship.
- The resulting line will allow you to estimate the Celsius temperature for any given Fahrenheit value.