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The problem asks to find the weighted average of the points \( W \), \( X \), and \( Y \) on the number line, where:

- Point \( W \) weighs twice as much as point \( X \),
- Point \( Y \) weighs three times as much as point \( X \).

Let's begin by identifying the coordinates of the points on the number line:

- \( W = -6 \),
- \( X = -3 \),
- \( Y = 1 \).

Let the weight of point \( X \) be \( 1 \) (since the weight is relative), which means:

- The weight of \( W \) is \( 2 \times 1 = 2 \),
- The weight of \( Y \) is \( 3 \times 1 = 3 \).

The formula for the weighted average is:

\[
P = \frac{(W \times \text{weight of } W) + (X \times \text{weight of } X) + (Y \times \text{weight of } Y)}{\text{sum of the weights}}
\]

Substituting the values:

\[
P = \frac{(-6 \times 2) + (-3 \times 1) + (1 \times 3)}{2 + 1 + 3}
\]

Let me calculate the result.The coordinate of point \( P \), representing the weighted average of points \( W \), \( X \), and \( Y \), is \( -2 \).

Would you like more details on how this was calculated or have any further questions?

Here are five related questions for practice:

1. What would the coordinate of \( P \) be if point \( Y \) weighed 4 times as much as point \( X \) instead of 3?
2. How would the result change if point \( X \) had a different weight?
3. Can you calculate the weighted average of four points on a number line?
4. What happens if all the points have equal weights?
5. How does changing the number line scale affect the weighted average?

**Tip:** When calculating a weighted average, always remember that the sum of the weights is crucial in determining the balance point.

Use the number line to find the coordinate of P that represents the weighted average of the set of points such that Point W weighs twice as much as point X, and point Y weighs three times as much as point X.

Find the weighted average of points W, X, and Y on a number line, where W weighs twice as much as X, and Y weighs three times as much as X. This math problem covers concepts of weighted averages and coordinate geometry. Suitable for students in Grades 6-8.

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