Question

Write the equation of the line that passes through (2, -6) and is perpendicular to y=2/3x+4

A. y = -x - 9
B. y = 3x-220
C. y = -x - 3
D. y = -x - 7
SHOW STEP BY STEP PLEASE ​

Answer 1

y = -3/2x - 3.

Explanation:

The line y = 2/3x + 4 has a slope of 2/3 so a line perpendicular to it has

a slope of -1 / 2/3 = -3/2.

So the required line has the equation:

y - y1 = -3/2(x - x1) where (x1, y1) is a point on this line.

Substituting x1 = 2 and y1 = -6, we have:

y - -6 = -3/2(x - 2)

y + 6 = -3/2x + 3

y = -3/2x - 3