To determine the equation of a line that is parallel to the given line [tex]\( x = -6 \)[/tex] and passes through the point [tex]\((-4, -6)\)[/tex], follow these steps:
1. Identify the nature of the given line: The equation [tex]\( x = -6 \)[/tex] represents a vertical line that passes through all points where the x-coordinate is [tex]\(-6\)[/tex]. This line is vertical and does not depend on the y-coordinate.
2. Understand what it means to be parallel: A line that is parallel to another line has the same orientation. Since the given line [tex]\( x = -6 \)[/tex] is vertical, any line parallel to it must also be vertical.
3. Find the equation of the parallel line: A vertical line parallel to [tex]\( x = -6 \)[/tex] will have the same form of equation, which is [tex]\( x = \text{constant} \)[/tex]. Because the new line must pass through the point [tex]\((-4, -6)\)[/tex], we need to find the specific constant value for [tex]\( x \)[/tex] in this situation.
4. ### Determine the constant value:
- Since the point [tex]\((-4, -6)\)[/tex] lies on the line we are trying to find, we use the x-coordinate of this point. Here, the x-coordinate is [tex]\(-4\)[/tex].
Therefore, the equation of the vertical line parallel to [tex]\( x = -6 \)[/tex] and passing through the point [tex]\((-4, -6)\)[/tex] is [tex]\( x = -4 \)[/tex].
So, the correct answer is [tex]\( x = -4 \)[/tex].
