Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.