To determine the equation of the line that is parallel to the given line and passes through the specified point, let's analyze the given information.
1. The given line is \( x = -6 \). This is a vertical line because the equation is in the form \( x = \text{constant} \). Vertical lines always have the form \( x = k \), where \( k \) is a constant value.
2. A line that is parallel to \( x = -6 \) must also be a vertical line since parallel lines have the same orientation. Therefore, the equation of the parallel line will be in the form \( x = k \).
3. Now, we need to determine the specific value of \( k \) such that the line passes through the given point, \((-4, -6)\). The vertical line passing through any point has the equation \( x = \text{the x-coordinate of the point} \).
4. Here, the x-coordinate of the point \((-4, -6)\) is \(-4\).
Therefore, the equation of the line that is parallel to \( x = -6 \) and passes through the point \((-4, -6)\) is:
[tex]\[ x = -4 \][/tex]
Hence, the correct answer is:
[tex]\[ x = -4 \][/tex]
