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The question asks, "Which equation represents a line that is perpendicular to the x-axis?" 

- A line that is perpendicular to the x-axis is a vertical line.
- Vertical lines have the form **\( x = \text{constant} \)**, where the value of \( x \) is fixed for all values of \( y \).

Looking at the options:
1. \( y = 4 \) - This represents a horizontal line.
2. \( y = x \) - This is the equation of a diagonal line with slope 1.
3. \( x = \frac{1}{2} y \) - This represents a line with a slope of 2.
4. \( x = 4 \) - This represents a vertical line.

### The correct answer is: **\( x = 4 \)**, as it represents a vertical line, which is perpendicular to the x-axis.

Would you like further details or explanations? Here are some related questions you could explore:

1. What is the general form of the equation of a vertical line?
2. How do you identify horizontal lines from an equation?
3. What is the slope of a line perpendicular to the x-axis?
4. How does the slope-intercept form help in identifying line orientation?
5. Can a vertical line have a slope?

**Tip:** Remember that vertical lines always have undefined slopes and are written as \( x = \text{constant} \), while horizontal lines have a slope of 0 and are written as \( y = \text{constant} \).

Which equation represents a line which is perpendicular to the x-axis?

Find out which equation represents a line perpendicular to the x-axis. This problem covers important geometry concepts such as vertical and horizontal lines and how to identify them using their equations. Suitable for students in Grades 8-10.

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