select the equation of the line passes through the point (2,6) and is perpendicular to the line x=4.
Answers
y=4
y=6
x=6
x=2
perpendicular to x = 4 is y = some constant (sketch it)
That constant is 6
y = 6
thanx damon
You are welcome.
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. Let's work through the steps:
1. Given the equation x = 4, we can see that the line is vertical, meaning it is parallel to the y-axis. In this case, the slope is undefined since vertical lines have no slope.
2. To find the slope of the line that is perpendicular to x = 4, we take the negative reciprocal of the undefined slope. The negative reciprocal of an undefined slope is 0.
3. Now that we have the slope (m = 0) and a point (2, 6) on the line, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point.
4. Plugging in the values from the given point and the slope, we get: y - 6 = 0(x - 2).
5. Simplifying the equation further, we have: y - 6 = 0.
6. Adding 6 to both sides of the equation, we get: y = 6.
Therefore, the correct equation of the line passing through the point (2, 6) and perpendicular to x = 4 is y = 6.
Hence, the answer is y = 6.