Let's determine if the equation \( x - 2y = 8 \) represents a line that is perpendicular to the line \( y = -\frac{1}{2}x - 6 \).

### Steps:
1. **Convert the equation \( x - 2y = 8 \) to slope-intercept form \( y = mx + b \)**:
   - Start by isolating \( y \) on one side of the equation.
   
   \[
   x - 2y = 8
   \]
   \[
   -2y = -x + 8
   \]
   \[
   y = \frac{1}{2}x - 4
   \]

   The slope \( m \) of this line is \( \frac{1}{2} \).

2. **Compare the slopes**:
   - The slope of the original line is \( -\frac{1}{2} \).
   - The slope of the line represented by \( x - 2y = 8 \) is \( \frac{1}{2} \).

3. **Check for perpendicularity**:
   - Two lines are perpendicular if the product of their slopes is \( -1 \).
   - The product of the slopes is:
   
   \[
   \left(-\frac{1}{2}\right) \times \frac{1}{2} = -\frac{1}{4}
   \]

   Since \( -\frac{1}{4} \) is not equal to \( -1 \), the lines are not perpendicular.

### Conclusion:
The equation \( x - 2y = 8 \) does not represent a line that is perpendicular to \( y = -\frac{1}{2}x - 6 \). Instead, a line perpendicular to \( y = -\frac{1}{2}x - 6 \) would have a slope of \( 2 \), so its equation should be in the form \( y = 2x + c \).

Would you like help finding the correct perpendicular line through a specific point or with any other questions?

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**Related Questions**:
1. How do you find the equation of a line given a slope and a point?
2. What does it mean when two lines are parallel?
3. How do you determine the slope from an equation in standard form?
4. Can a vertical line be perpendicular to a horizontal line?
5. How do you find the y-intercept of a line from an equation?
6. What is the slope-intercept form of a line?
7. How do you graph a line using its slope and y-intercept?
8. What is the relationship between the slopes of parallel and perpendicular lines?

**Tip**: Always check the slopes of two lines to determine if they are perpendicular; their slopes must multiply to \( -1 \).

Explore whether the equation x - 2y = 8 represents a line perpendicular to y = -1/2x - 6. Learn how to compare slopes, apply the rule for perpendicular lines, and find the correct line equation. Suitable for high school students studying linear equations.

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