To find the weighted average of the points on the line, we need to account for both the position of the points and their respective weights.

• There are two points:
  • One at $x = -4$ with a weight of 2.
  • One at $x = 2$ with a weight of 8.

The formula for the weighted average is:

$\text{Weighted Average} = \frac{(x_1 \cdot w_1) + (x_2 \cdot w_2)}{w_1 + w_2}$

Where:

• $x_1 = -4$, $w_1 = 2$
• $x_2 = 2$, $w_2 = 8$

Now, let's calculate it:

$\text{Weighted Average} = \frac{(-4 \cdot 2) + (2 \cdot 8)}{2 + 8} = \frac{-8 + 16}{10} = \frac{8}{10} = 0.8$

The weighted average is $0.8$.

Would you like further details or have any questions about this solution?

Here are some related questions to explore further:

1. How is a weighted average different from a simple average?
2. How does increasing the weight of one point affect the weighted average?
3. Can a weighted average be negative? If so, when?
4. How would the weighted average change if the points were closer to each other?
5. What are real-life examples of using weighted averages?

Tip: Weighted averages are often used when different data points have varying levels of importance or frequency.