Answer :
Sure! Let's address the problem step-by-step for each line.
1. Line \( y = -2 \):
- The given equation is a horizontal line where every point on the line has y-coordinate \(-2\).
- A line parallel to \( y = -2 \) is also a horizontal line and will have the equation \( y = k \), where \( k \) is a constant.
- Possible parallel line equations: \( y = -2 \) and \( y = -4 \).
2. Line \( x = -2 \):
- The given equation is a vertical line where every point on the line has x-coordinate \(-2\).
- A line parallel to \( x = -2 \) is also a vertical line and will have the equation \( x = k \), where \( k \) is a constant.
- Possible parallel line equations: \( x = -2 \) and \( x = -4 \).
3. Line \( y = -4 \):
- The given equation is a horizontal line where every point on the line has y-coordinate \(-4\).
- A line parallel to \( y = -4 \) is also a horizontal line and will have the equation \( y = k \), where \( k \) is a constant.
- Possible parallel line equations: \( y = -4 \) and \( y = -2 \).
4. Line \( x = -4 \):
- The given equation is a vertical line where every point on the line has x-coordinate \(-4\).
- A line parallel to \( x = -4 \) is also a vertical line and will have the equation \( x = k \), where \( k \) is a constant.
- Possible parallel line equations: \( x = -4 \) and \( x = -2 \).
So, the equations of the lines that are parallel to the given lines are:
- For \( y = -2 \): Parallel line equations are \( y = -2 \) and \( y = -4 \).
- For \( x = -2 \): Parallel line equations are \( x = -2 \) and \( x = -4 \).
- For \( y = -4 \): Parallel line equations are \( y = -4 \) and \( y = -2 \).
- For \( x = -4 \): Parallel line equations are \( x = -4 \) and \( x = -2 \).
Summarizing the results:
- \( y = -2 \)
- \( x = -2 \)
- \( y = -4 \)
- \( x = -4 \)
These represent the lines parallel to the original given lines.
1. Line \( y = -2 \):
- The given equation is a horizontal line where every point on the line has y-coordinate \(-2\).
- A line parallel to \( y = -2 \) is also a horizontal line and will have the equation \( y = k \), where \( k \) is a constant.
- Possible parallel line equations: \( y = -2 \) and \( y = -4 \).
2. Line \( x = -2 \):
- The given equation is a vertical line where every point on the line has x-coordinate \(-2\).
- A line parallel to \( x = -2 \) is also a vertical line and will have the equation \( x = k \), where \( k \) is a constant.
- Possible parallel line equations: \( x = -2 \) and \( x = -4 \).
3. Line \( y = -4 \):
- The given equation is a horizontal line where every point on the line has y-coordinate \(-4\).
- A line parallel to \( y = -4 \) is also a horizontal line and will have the equation \( y = k \), where \( k \) is a constant.
- Possible parallel line equations: \( y = -4 \) and \( y = -2 \).
4. Line \( x = -4 \):
- The given equation is a vertical line where every point on the line has x-coordinate \(-4\).
- A line parallel to \( x = -4 \) is also a vertical line and will have the equation \( x = k \), where \( k \) is a constant.
- Possible parallel line equations: \( x = -4 \) and \( x = -2 \).
So, the equations of the lines that are parallel to the given lines are:
- For \( y = -2 \): Parallel line equations are \( y = -2 \) and \( y = -4 \).
- For \( x = -2 \): Parallel line equations are \( x = -2 \) and \( x = -4 \).
- For \( y = -4 \): Parallel line equations are \( y = -4 \) and \( y = -2 \).
- For \( x = -4 \): Parallel line equations are \( x = -4 \) and \( x = -2 \).
Summarizing the results:
- \( y = -2 \)
- \( x = -2 \)
- \( y = -4 \)
- \( x = -4 \)
These represent the lines parallel to the original given lines.
