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What is the equation of the line that is parallel to the given line and passes through the given point?

Given line: [tex]y = -2[/tex]

Point: [tex](x, y) = (-2, -4)[/tex]

The equation of the parallel line is:

A. [tex]y = -2[/tex]
B. [tex]x = -2[/tex]
C. [tex]y = -4[/tex]
D. [tex]x = -4[/tex]

Sagot :

GinnyAnswer
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.
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