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The problem is asking for the result of reflecting the point \((-2, -6)\) across the line \(y = x\), and then determining the new \(y\)-value of the reflected point.

To reflect a point \((x, y)\) across the line \(y = x\), you simply swap the coordinates. That is, the point \((x, y)\) becomes \((y, x)\) after the reflection.

Given the point \((-2, -6)\), after reflecting across \(y = x\), the new coordinates will be \((-6, -2)\).

So, the \(y\)-value after the reflection is \(-2\).

Would you like a detailed explanation or any further questions?

Here are some related questions for practice:
1. What would the \(x\)-value be after reflecting \((3, 5)\) over \(y = x\)?
2. How do you reflect a point over the line \(y = -x\)?
3. If you reflect the point \((4, -7)\) across the line \(y = x\), what will the new coordinates be?
4. What happens to the distance from the origin when a point is reflected over \(y = x\)?
5. Can you describe the general rule for reflecting any point over the line \(y = x\)?

**Tip**: When reflecting points, always identify the line of reflection first; for \(y = x\), just swap the coordinates!

What is the y-value after performing the reflection of the point (-2, -6) across the line y = x?

This math problem demonstrates how to reflect the point (-2, -6) across the line y = x. Learn the step-by-step process of swapping coordinates to get the new y-value of -2. Suitable for students in Grades 8-10.

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