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:

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

$\{(-2, 3.9), (-1, 1.8), (0, 0.1), (1, -1.9), (2, -3.8)\}$

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.