To find the equation of a line that is parallel to a given line and passes through a specific point, let's follow these steps:
1. Identify the nature of the given line:
The given line is [tex]\( x = -6 \)[/tex]. This is a vertical line where all points on the line have an [tex]\( x \)[/tex]-coordinate of [tex]\(-6\)[/tex].
2. Determine the orientation of the parallel line:
Since parallel lines have the same orientation, the line parallel to [tex]\( x = -6 \)[/tex] will also be a vertical line. Therefore, the equation of the parallel line will be in the form [tex]\( x = c \)[/tex], where [tex]\( c \)[/tex] is a constant.
3. Find the [tex]\( x \)[/tex]-coordinate of the point the line passes through:
The given point through which the parallel line passes is [tex]\((-4, -6)\)[/tex]. The [tex]\( x \)[/tex]-coordinate of this point is [tex]\(-4\)[/tex].
4. Formulate the equation of the parallel line:
As the line we need to find is parallel to [tex]\( x = -6 \)[/tex] and passes through the point [tex]\((-4, -6)\)[/tex], the equation of this parallel line must have the [tex]\( x \)[/tex]-coordinate of [tex]\(-4\)[/tex]. Therefore, the equation of the line is:
[tex]\[
x = -4
\][/tex]
So, the equation of the line that is parallel to the given line [tex]\( x = -6 \)[/tex] and passes through the point [tex]\((-4, -6)\)[/tex] is:
[tex]\[
\boxed{x = -4}
\][/tex]
