To solve the problem of finding the equation of a line that is parallel to a given line and passes through a specific point, follow these steps:
1. Identify the given line and its characteristics:
The given line is [tex]\( x = -6 \)[/tex]. This line is a vertical line that crosses the x-axis at [tex]\( x = -6 \)[/tex].
2. Understanding parallel lines:
For two lines to be parallel, they must have the same slope. Vertical lines have an undefined slope, and any vertical line will be parallel to another vertical line because they all have the same orientation.
3. Determine the parallel line:
Given that we need a line parallel to [tex]\( x = -6 \)[/tex], the parallel line will also be a vertical line. The equation of a vertical line is always of the form [tex]\( x = \text{constant} \)[/tex].
4. Find the specific vertical line passing through the given point:
The provided point is [tex]\( (-4, -6) \)[/tex]. Since we need a vertical line that passes through [tex]\( (-4, -6) \)[/tex], the x-coordinate of the line must be equal to [tex]\( -4 \)[/tex].
Combining these steps, we conclude that the equation of the line that is parallel to [tex]\( x = -6 \)[/tex] and passes through the point [tex]\( (-4, -6) \)[/tex] is:
[tex]\[ x = -4 \][/tex]
So, the correct equation is [tex]\( x = -4 \)[/tex].
