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Founder  Joined: 18 Apr 2015
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Which of the following is an equation of a line that is perp [#permalink]
Expert's post 00:00

Question Stats: 36% (00:35) correct 63% (01:00) wrong based on 22 sessions

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
[Reveal] Spoiler: OA

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Director Joined: 03 Sep 2017
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Re: Which of the following is an equation of a line that is perp [#permalink]
To be perpendicular, the line must have a slope opposite and reciprocal to the one of the given line. Since the slope of the given line can be found to be -2/3 by dividing both sides of the equation by 3, the perpendicular line must have a slope of 3/2.

This is the case with choices B and D!
Director Joined: 20 Apr 2016
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Re: Which of the following is an equation of a line that is perp [#permalink]
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

[Reveal] Spoiler: OA
B and D

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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