To complete the table using a trend line equation and the correlation coefficient, you'll need the actual equation of the trend line. However, you haven't provided the specific data points or the form of the trend line equation (e.g., linear, quadratic, etc.).
If you have a dataset and have created a trend line using Desmos, the typical steps would be as follows:
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Determine the Trend Line Equation: In Desmos, you can fit a trend line to your data points. The trend line's equation will usually be in the form \( y = mx + b \) for linear relationships, where \( m \) is the slope and \( b \) is the y-intercept.
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Use the Correlation Coefficient (r): The correlation coefficient indicates the strength and direction of a linear relationship between two variables. A correlation of 0.87 suggests a strong positive linear relationship.
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Fill the Table: Use the trend line equation to calculate the predicted \( y \) values for each corresponding \( x \) value in your table. You will plug the \( x \) values into the equation to find the \( y \) values.
For example, if your trend line was \( y = 2x + 3 \), and your table had the following \( x \) values:
| x | Predicted y | |----|-------------| | 1 | | | 2 | | | 3 | |
You would calculate:
- For \( x = 1 \): \( y = 2(1) + 3 = 5 \)
- For \( x = 2 \): \( y = 2(2) + 3 = 7 \)
- For \( x = 3 \): \( y = 2(3) + 3 = 9 \)
And complete your table:
| x | Predicted y | |----|-------------| | 1 | 5 | | 2 | 7 | | 3 | 9 |
If you provide the specific trend line equation and the x-values from your dataset, I can help you fill out the table accordingly.