find the line that passes through (2,-5) and perpendicular to x=4
To find the line that passes through (2, -5) and is perpendicular to x = 4, we need to find the equation of the line.
Given that the line x = 4 is vertical (parallel to the y-axis), any line that is perpendicular to it will be horizontal (parallel to the x-axis) and will have an equation of the form y = c, where c is a constant.
Since the line passes through (2, -5), we have y = -5.
Therefore, the equation of the line that passes through (2, -5) and is perpendicular to x = 4 is y = -5.
To find the line that passes through the point (2, -5) and is perpendicular to the line x = 4, we need to determine the slope of the perpendicular line.
The line x = 4 is a vertical line with an undefined slope. Any line perpendicular to it will have a slope of 0.
Therefore, the line passing through (2, -5) and perpendicular to x = 4 will have a slope of 0.
We can use the point-slope form of a line to find the equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Plugging in the coordinates (2, -5) and slope 0, we get:
y - (-5) = 0(x - 2)
y + 5 = 0
Simplifying further, we get the equation:
y = -5
So, the line that passes through (2, -5) and is perpendicular to x = 4 is the horizontal line y = -5.
To find the line that passes through the point (2, -5) and is perpendicular to the line x = 4, we need to determine the equation of the perpendicular line.
First, we observe that the line x = 4 is a vertical line passing through the x-coordinate 4. A line perpendicular to a vertical line is a horizontal line, where the y-coordinate remains constant.
Since the line we're looking for passes through the point (2, -5), the y-coordinate must be -5. Therefore, the equation of the line perpendicular to x = 4 and passing through (2, -5) is y = -5.
So, the line that passes through (2, -5) and is perpendicular to x = 4 is the horizontal line with the equation y = -5.