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The image shows two sets of points where you're asked to find the equation of a trend line (line of best fit) for each. Let's calculate the equation of the trend lines using the least-squares method.

The two sets of points are:

3. 
\[
\{(1, 2.1), (3, 3.1), (5, 4.0), (7, 5.2), (9, 5.9)\}
\]

4.
\[
\{(-2, 3.9), (-1, 1.8), (0, 0.1), (1, -1.9), (2, -3.8)\}
\]

I'll calculate the trend lines for both sets of points, providing the equations in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Let me proceed with the calculations.The equations of the trend lines for the two sets of points are:

3. The equation of the trend line is:
\[
y = 0.485x + 1.635
\]

4. The equation of the trend line is:
\[
y = -1.91x + 0.02
\]

These equations represent the lines that best fit the given points in each set.

Would you like further clarification on the process or any more details?

Here are 5 questions related to the concept of trend lines:
1. What is the significance of the slope in a trend line equation?
2. How is the y-intercept interpreted in the context of trend lines?
3. What does the \(R^2\) value represent in the context of linear regression?
4. How can you determine if a linear trend line is a good fit for a given set of points?
5. What is the impact of outliers on the accuracy of a trend line?

**Tip**: The slope \(m\) in a trend line represents the rate of change of \(y\) with respect to \(x\). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing one.

Write the equation of a trend line, if possible. 3. {(1, 2.1), (3, 3.1), (5, 4.0), (7, 5.2), (9, 5.9)} 4. {(−2, 3.9), (−1, 1.8), (0, 0.1), (1, −1.9), (2, −3.8)}

Learn how to find the equation of a trend line for two sets of points using linear regression. We cover the least squares method, including detailed steps to find the slope and y-intercept. Suitable for students in Grades 10-12.

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