The coordinate plane below shows point P(-2,2) and the line y= 2/3x -1.
.
On the coordinate x-y plane, a rectangle has the coordinates at (-2, 3), (5, 3), (-2, -2) and (5, -2).
Which equation describes the line that passes through point P and is perpendicular to the line on the graph?
A. y= -2/3x - 2/3
B. y= -2/3x - 1
C. y= -2/3x + 2/3
D. y= -2/3x + 1
To find the line that passes through point P and is perpendicular to the given line y= 2/3x -1, we need to find the negative reciprocal of the slope of the given line. The slope of the given line is 2/3, so the negative reciprocal is -3/2.
The general form of the equation of a line is y=mx + b, where m is the slope and b is the y-intercept.
Since we know the point P(-2,2), we can substitute these coordinates into the equation to solve for b:
2 = (-3/2)(-2) + b
2 = 3 + b
b = -1
So, the equation of the line passing through point P and perpendicular to the given line is y= -3/2x - 1.
Therefore, the correct answer is:
D. y= -2/3x + 1