Which of the following is an equation of a line that is perpendicular

Question

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

I. 3x— 2y = 4

II. 2x— 3y = 4

III. 4 — 3x= —2y

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

LeoN88 · Answer

For y=mx + c, Two lines are perpendicular provided their slopes: m1*m2= -1

Slope of given line: (-2/3)
Slope of lines:
I (3/2)
II (2/3)
III (3/2)

So  only I and III  satisfies m1*m2= -1.

GmatPrime · Answer

Linear equation 
y = mx + c (where, m is slope and c is constant/y-intercept)

Let's find the slope of the line in question,
2x+3y=4
y= (-2x+4) / 3
slope= -2/3

For  perpendicular line ,  slope  is of  opposite sign and reciprocal

Let's analyze statements
St. 1
3x— 2y = 4
y = (-3x+4) / (-2)
Slope = 3/2

St.2 
2x— 3y = 4
y = (-2x+4) / (-3)
Slope = 2/3

St. 3 
4 — 3x= —2y
y = (-3x+4) / (-2)
Slope = 3/2

Only St. 1 & 3 have opposite signs and are reciprocal of -2/3

Option D is the answer

AyushCrackVerbal · Answer

Given equation:

2x + 3y = 4

The slope of the above equation = -(coefficient of y/ coefficient of x) = -3/2

As we know, the product of the slopes of the two perpendicular lines is 1.

The slope of the line perpendicular to the given line would be 2/3.

Now, let us check the slope of the lines given:

3x - 2y = 4 : Slope = 2/3

2x - 3y = 4 : Slope = 3/2

4 - 3x = -2y ; Writing this equation in the standard form :  2y - 3x = -4 : Slope = 2/3

So the slope of equation I and III is 2/3.

The correct answer is  D

Archit3110 · Answer

m1*m2=-1
so m1= -2/3
we need m2=3/2
which is in III. 4 — 3x= —2y & I. 3x— 2y = 4 
IMO D

AbhaGanu · Answer

AyushCrackVerbal  is this the general formula we can use : The slope of the above equation = -(coefficient of y/ coefficient of x) = -3/2

SSG12 · Answer

Solution to the question is given in the attachment -

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