Write the equation of a line that is perpendicular to the given line and that passes through the given point. y – 3 = (x + 2); (–2, 3) (1 point) Responses y + 3 = –(x – 2) y + 3 = – Image with alt text: three-eighths ( x – 2) y – 3 = –(x + 2) y – 3 = – Image with alt text: three-eighths ( x + 2) y – 2 = –(x + 3) y – 2 = – Image with alt text: three-eighths ( x + 3) y + 3 = (x – 2)
The given line has a slope of 1.
Perpendicular lines have slopes that are negative reciprocals of each other.
So, the perpendicular line will have a slope of -1.
Let's use the point-slope form to find the equation of the line passing through (-2, 3) with a slope of -1.
Using the point-slope form, we have:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is the given point.
Using the point (-2, 3), the equation becomes:
y - 3 = -1(x - (-2))
Simplifying:
y - 3 = -1(x + 2)
Now, let's rewrite this equation in the standard form:
y - 3 = -x - 2
Adding x to both sides:
x + y - 3 = -2
Rearranging the terms:
x + y = -1
So, the equation of the line perpendicular to y – 3 = (x + 2) and passing through (-2, 3) is x + y = -1.
To find the equation of a line perpendicular to another line, we need to determine the negative reciprocal slope of the given line.
The given line has a slope of 1/8 (by rearranging the equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept).
The negative reciprocal of 1/8 is -8/1 or -8.
Now, we have the slope (-8) and the point (–2, 3) that the perpendicular line passes through. We can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Plugging in the values, we get:
y - 3 = -8(x - (-2))
y - 3 = -8(x + 2)
Therefore, the equation of the line perpendicular to y – 3 = (x + 2) and passing through (–2, 3) is:
y - 3 = -8(x + 2)
To find the equation of a line perpendicular to the given line and passing through the given point, we need to use the slope-intercept form of a line, which is given by y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's determine the slope of the given line. The equation y - 3 = (x + 2) is in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line. Comparing it with the slope-intercept form, we can see that the slope of the given line is 1.
To find the slope of a line perpendicular to the given line, we use the fact that perpendicular lines have slopes that are negative reciprocals. So, the slope of the perpendicular line is -1/m.
Since m = 1, the slope of the perpendicular line is -1/1, which simplifies to -1.
Now that we have the slope of the perpendicular line, we can plug it into the point-slope form of a line to find the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point.
Using the given point (–2, 3), the equation becomes y - 3 = -1(x - (-2)), which simplifies to y - 3 = -1(x + 2).
Therefore, the equation of the line perpendicular to y - 3 = (x + 2) and passing through the point (–2, 3) is y - 3 = -1(x + 2).