To find the equations of lines that are parallel to the given lines and pass through the specified points, let's analyze each line and its parallel counterpart step-by-step.
### Equation 1: Line [tex]\( y = -2 \)[/tex]
This line is a horizontal line where the y-coordinate is always [tex]\(-2\)[/tex] regardless of the x-coordinate.
We need to find a parallel line that passes through a given point, specifically [tex]\(y = -4\)[/tex].
#### Solution:
A line that is parallel to [tex]\( y = -2 \)[/tex] will also be a horizontal line. To pass through [tex]\( y = -4 \)[/tex], the equation of this line is:
[tex]\[ y = -4 \][/tex]
### Equation 2: Line [tex]\( x = -2 \)[/tex]
This line is a vertical line where the x-coordinate is always [tex]\(-2\)[/tex] regardless of the y-coordinate.
We need to find a parallel line that passes through a given point, specifically [tex]\( x = -4 \)[/tex].
#### Solution:
A line that is parallel to [tex]\( x = -2 \)[/tex] will also be a vertical line. To pass through [tex]\( x = -4 \)[/tex], the equation of this line is:
[tex]\[ x = -4 \][/tex]
So, summarizing the parallel line equations that pass through the specified points:
1. The line parallel to [tex]\( y = -2 \)[/tex] passing through [tex]\( y = -4 \)[/tex] is [tex]\( y = -4 \)[/tex].
2. The line parallel to [tex]\( x = -2 \)[/tex] passing through [tex]\( x = -4 \)[/tex] is [tex]\( x = -4 \)[/tex].
Therefore, the equations of the lines are:
[tex]\[ y = -4 \][/tex]
[tex]\[ x = -4 \][/tex]
The result is [tex]\((-4, -4)\)[/tex].
