Sure! To find the equation of a line that is parallel to a given line and passes through a specific point, we need to first understand the properties of the given line.
1. Identify the given line: In this case, let's denote the given line as a vertical line. Vertical lines have an equation of the form \( x = c \), where \( c \) is the x-coordinate of any point on the line.
2. Understand parallel lines: For two lines to be parallel, their slopes must be identical. Vertical lines are parallel to each other because they both have undefined slopes. Hence, any line parallel to a vertical line will also be vertical.
3. Given point: The point through which the new line must pass is \((-4, -6)\).
4. Equation of parallel line: Since the line is vertical and must pass through the point \((-4, -6)\), the x-coordinate is always \(-4\).
Thus, the equation of the line that is parallel to the given vertical line and passes through the point \((-4, -6)\) is:
[tex]\[ x = -4 \][/tex]
Hence, the correct answer is:
[tex]\[ x = -4 \][/tex]
