Write the equation of a line that is perpendicular to 
\[x=3\] and that passes through the point 
\[(0,-4)\].

The equation \(x = 3\) represents a vertical line. A line that is perpendicular to a vertical line is a horizontal line. Horizontal lines have the form:

\[
y = c
\]

where \(c\) is a constant representing the \(y\)-coordinate of all points on the line. Since the perpendicular line must pass through the point \((0, -4)\), the \(y\)-coordinate of the line is \(-4\). 

Thus, the equation of the line is:

\[
y = -4
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you determine the slope of a line perpendicular to a vertical line?
2. What is the slope of a vertical line like \(x = 3\)?
3. How would you write the equation of a line perpendicular to \(y = 2\)?
4. Can you write the equation of a line passing through \((0, -4)\) that is not perpendicular to \(x = 3\)?
5. How would the graph of \(y = -4\) look on a coordinate plane?

**Tip:** The slope of a vertical line is undefined, while the slope of a horizontal line is always zero.

Write the equation of a line that is perpendicular to x = 3 and that passes through the point (0, -4).

Learn how to find the equation of a line that is perpendicular to x = 3 and passes through the point (0, -4). This problem involves understanding perpendicular lines, vertical and horizontal slopes, and applying the equation of a horizontal line. Suitable for Grades 7-8.

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