Question

What is the equation of the line that is perpendicular to y=-2/3x+4 and that passes through (-2,2)?

A. Y=3/2x-10/3
B.y=3/2x-5
C. Y=3/2x+1
D. Y=3/2x- 2/3

Answer 1

The equation of the line perpendicular to y = -2/3x + 4 and passing through (-2,2) is y = (3/2)x - 5.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line. The given line has a slope of -2/3, so the perpendicular line will have a slope of 3/2. Next, we can use the point-slope form of the equation of a line to find the equation of the perpendicular line. Plugging in the coordinates (-2,2) and the slope 3/2 into the point-slope form, we get the equation y = (3/2)x - 5.