https://file.aiquickdraw.com/mathbot/file/1726497334407gs0f71kz.jpg

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.

Find the weighted average of the points on the line: One point at x = -4 with a weight of 2 and another at x = 2 with a weight of 8.

Learn how to calculate the weighted average of two points on a number line with different weights. The problem involves points at x = -4 (weight 2) and x = 2 (weight 8). This solution covers key algebraic concepts and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation