Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our 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.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.