Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the equation of the line that is perpendicular to the given line and passes through the point [tex]\((2, 6)\)[/tex], let's proceed step-by-step:
1. Identify the nature of the given line:
The given line is [tex]\(x = 2\)[/tex]. This is a vertical line because in this equation, the x-coordinate is always 2, regardless of the y-coordinate.
2. Understand perpendicular lines:
A line perpendicular to a vertical line must be horizontal. This is because a vertical line has an undefined slope, and the slope of a perpendicular line (in this case) must be the negative reciprocal, which translates to a zero slope. A line with a zero slope is horizontal.
3. Equation of a horizontal line:
The equation of a horizontal line takes the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is the y-coordinate that the line passes through.
4. Determine the y-coordinate:
The line must pass through the point [tex]\((2, 6)\)[/tex]. Since it is horizontal, it will maintain the same y-coordinate for all values of x.
5. Form the equation:
Given that the point [tex]\((2, 6)\)[/tex] has a y-coordinate of 6, the equation of the horizontal line passing through this point is simply:
[tex]\[ y = 6 \][/tex]
Therefore, the equation of the line that is perpendicular to the given vertical line [tex]\(x = 2\)[/tex] and passes through the point [tex]\((2, 6)\)[/tex] is [tex]\(y = 6\)[/tex].
Thus, the correct answer is:
[tex]\[ y = 6 \][/tex]
1. Identify the nature of the given line:
The given line is [tex]\(x = 2\)[/tex]. This is a vertical line because in this equation, the x-coordinate is always 2, regardless of the y-coordinate.
2. Understand perpendicular lines:
A line perpendicular to a vertical line must be horizontal. This is because a vertical line has an undefined slope, and the slope of a perpendicular line (in this case) must be the negative reciprocal, which translates to a zero slope. A line with a zero slope is horizontal.
3. Equation of a horizontal line:
The equation of a horizontal line takes the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is the y-coordinate that the line passes through.
4. Determine the y-coordinate:
The line must pass through the point [tex]\((2, 6)\)[/tex]. Since it is horizontal, it will maintain the same y-coordinate for all values of x.
5. Form the equation:
Given that the point [tex]\((2, 6)\)[/tex] has a y-coordinate of 6, the equation of the horizontal line passing through this point is simply:
[tex]\[ y = 6 \][/tex]
Therefore, the equation of the line that is perpendicular to the given vertical line [tex]\(x = 2\)[/tex] and passes through the point [tex]\((2, 6)\)[/tex] is [tex]\(y = 6\)[/tex].
Thus, the correct answer is:
[tex]\[ y = 6 \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.