To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line and take the negative reciprocal of it.
The given line can be rewritten in slope-intercept form as y = x + 5.
Comparing this equation to the standard slope-intercept form y = mx + b, we can determine that the slope of the given line is m = 1.
To find the slope of the perpendicular line, we take the negative reciprocal of 1.
So, the slope of the perpendicular line is m = -1.
Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (–2, 3), we can substitute the values to find the equation of the line.
Plugging in x1 = -2, y1 = 3, and m = -1 into the point-slope form, we get:
y - 3 = -1(x - (-2))
y - 3 = -1(x + 2)
y - 3 = -x - 2
Rearranging the equation to slope-intercept form, we get:
y = -x + 1
Therefore, the equation of the line that is perpendicular to y – 3 = (x + 2) and passes through the point (–2, 3) is: y = -x + 1.
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)
A. y + 3 = – 3/8(x – 2)
B. y – 3 = – 3/8(x + 2)
C. y – 2 = –(x + 3)
D. y + 3 = 3/8 (x – 2)
1 answer
1 answer