Write an equation of the line that pass through point P and is perpendicular to the line with the given equation.
P(3,5); y=4
This is a horizontal line, so a perpendicular line gives you a constant x value, providing the equation x=3
y=1/4
To find the equation of the line that passes through point P(3, 5) and is perpendicular to the line with the equation y = 4, we need to find the slope of the given line first.
The equation y = 4 represents a horizontal line with a constant y-value of 4. Since the slope of a horizontal line is always 0, the slope of the given line is 0.
Perpendicular lines have slopes that are negative reciprocals of each other. To find the slope of the line perpendicular to y = 4, we take the negative reciprocal of 0, which is undefined. Therefore, the slope of the new line is undefined.
When a line has an undefined slope, it means that it is a vertical line. Since the line passes through point P(3, 5), the equation of the line that is perpendicular to y = 4 and passes through P(3, 5) can be written as x = 3.
To find the equation of a line that is perpendicular to the given line, we need to find its slope first.
The given line's equation is y=4, which means the line is horizontal and has a slope of 0 since the y-coordinate does not change.
To find the slope of a line perpendicular to a horizontal line, we need to find the slope of a vertical line. Keep in mind that the slope of a vertical line is undefined. Since a horizontal line has a slope of 0, a vertical perpendicular line will have an undefined slope.
Now that we know the slope of the line perpendicular to the given line, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substitute the values of point P into the equation:
y - 5 = undefined(x - 3)
Since the slope is undefined, the equation becomes:
y - 5 = undefined
And after simplifying, we get:
y = 5
Therefore, the equation of the line that passes through point P(3, 5) and is perpendicular to the line y = 4 is y = 5.