Carcass wrote:

Which of the following is an equation of a line that is perpendicular to the line whose equation is 2x+ 3y= 4?

Indicate all such equations.

A) 3x+ 2y= 4

B) 3x— 2y = 4

C) 2x— 3y = 4

D) 4 — 3x= —2y

E) 4 + 2x = 3y

Two lines are perpendicular when the slope of one line is the negative reciprocal of the other.

If one line has a slope \(m\), then the other line must have a slope\(\frac{-1}{m}\)so that two lines are perpendicular.

Here the equation 2x+ 3y= 4

or we can re write in y= mx +b form

or 3y = -2x +4

or\(y= \frac{-2}{3} x +4\)

Here slope m = -2/3

Now the other line must have a slope of 3/2.

So looking at the equation option B

if we re write the equ in y = mx + b form we have

\(2y = 3x +4\)

or \(y = \frac{3}{2} x - 4\)

here slope m = 3/2

In equ D we re write the equ in y = mx + b form we have

\(2y = 3x + 4\)

or \(y = \frac{3}{2} x -4\).

Therefore option B and Option D are our possible answer

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