The coordinate plane below shows point P(-2,2) and the line y= 2/3x -1.
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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
The line that passes through point P and is perpendicular to the line y = 2/3x - 1 will have a slope that is the negative reciprocal of 2/3. The negative reciprocal of 2/3 is -3/2.
Therefore, the equation that describes the line passing through point P and is perpendicular to the given line is:
y = -3/2x + b
To find the value of b, we can substitute the coordinates of point P (-2, 2) into the equation:
2 = -3/2(-2) + b
2 = 3 + b
b = -1
Therefore, the equation of the line is:
y = -3/2x - 1
The correct answer is B. y = -3/2x - 1.