To determine if the lines \(2 - x\) and \(x + 2\) are perpendicular, we need to compare their slopes. For two lines to be perpendicular, the product of their slopes should be \(-1\).

1. **Rewrite equations in slope-intercept form \(y = mx + b\):**

   - For the line \(y = 2 - x\), it's already in slope-intercept form. Here, the slope (\(m\)) is \(-1\).
   - For the line \(y = x + 2\), it's also in slope-intercept form with the slope (\(m\)) being \(1\).

2. **Check the product of the slopes:**

   - The slopes are \(-1\) and \(1\).
   - The product of these slopes is: 
     \[
     (-1) \times 1 = -1.
     \]

Since the product of the slopes is \(-1\), the lines \(y = 2 - x\) and \(y = x + 2\) are indeed perpendicular.

Would you like further details or have any questions? Here are some related questions:

1. What does the slope of a line represent in geometry?
2. How can you find the slope from a line given in standard form?
3. What are parallel lines and how can you identify them?
4. How do you find the point of intersection between two lines?
5. What is the significance of perpendicular lines in coordinate geometry?

**Tip:** For perpendicular lines, always check if the slopes are negative reciprocals of each other!

Explore how to determine if the lines 2 - x and x + 2 are perpendicular by analyzing their slopes. This guide walks through key geometry and algebra concepts, including slope calculation and the condition for perpendicularity. Suitable for students in Grades 8-10.

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