Answer :
To solve the problem of finding the equation of a line that is perpendicular to the given line and passes through the point (2, 6), we start by analyzing the given line.
1. Analyze the Given Line:
- The equation [tex]\(x = 2\)[/tex] represents a vertical line. This line is vertical and passes through all points where [tex]\( x = 2 \)[/tex].
2. Determine the Perpendicular Line:
- A line perpendicular to a vertical line is a horizontal line. Therefore, we are looking for a horizontal line that passes through a specific point.
3. Identify the Point of Intersection:
- We need the perpendicular line to pass through the point (2, 6).
4. Equation of the Horizontal Line:
- The equation of a horizontal line is of the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is a constant representing the y-value of all points on the line.
- Since the line must pass through the point (2, 6), the y-value for the equation of this line will be 6.
5. Write the Equation:
- Therefore, the equation of the line that is perpendicular to [tex]\(x = 2\)[/tex] and passes through the point (2, 6) is [tex]\(y = 6\)[/tex].
Thus, the correct equation of the line is:
[tex]\[ y = 6 \][/tex]
1. Analyze the Given Line:
- The equation [tex]\(x = 2\)[/tex] represents a vertical line. This line is vertical and passes through all points where [tex]\( x = 2 \)[/tex].
2. Determine the Perpendicular Line:
- A line perpendicular to a vertical line is a horizontal line. Therefore, we are looking for a horizontal line that passes through a specific point.
3. Identify the Point of Intersection:
- We need the perpendicular line to pass through the point (2, 6).
4. Equation of the Horizontal Line:
- The equation of a horizontal line is of the form [tex]\(y = c\)[/tex], where [tex]\(c\)[/tex] is a constant representing the y-value of all points on the line.
- Since the line must pass through the point (2, 6), the y-value for the equation of this line will be 6.
5. Write the Equation:
- Therefore, the equation of the line that is perpendicular to [tex]\(x = 2\)[/tex] and passes through the point (2, 6) is [tex]\(y = 6\)[/tex].
Thus, the correct equation of the line is:
[tex]\[ y = 6 \][/tex]
