In the coordinate system above, which of the following is the equation : Problem Solving (PS)

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In the coordinate system above, which of the following is the equation [#permalink]

12 Nov 2019, 12:58

line (l): ax + by = c (same as answer choice form)

(3,0) is on line (l): 3a = c
(0,2) is on line (l): 2b = c
=> 3a = 2b
=> a/b = 2/3
fits (B)

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Re: In the coordinate system above, which of the following is the equation [#permalink]

15 Nov 2019, 23:26

Bunuel wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Notice that line l passes through points (3,0) and (0,2), so its slope is \(m=\frac{y_2-y_1}{x_2-x_1}=-\frac{2}{3}\) (given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is \(m=\frac{y_2-y_1}{x_2-x_1}\)).

Only option B, when written in \(y=mx+b\) form has the slope of -2/3.

Answer: B.

can we assume initially that line is passing from 2nd QD to 4th QD so the slope should be neagtive and B & C are the only options satisfying it and then substitute the values of (3,0) and (0,2) to solve it ?

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Re: In the coordinate system above, which of the following is the equation [#permalink]

21 Apr 2020, 18:34

Quote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

Hello experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, AaronPond, GMATinsight, JeffTargetTestPrep, ccooley
Are the points Exactly in (3,0) and (0,2)?
Thanks__

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Re: In the coordinate system above, which of the following is the equation [#permalink]

23 Apr 2020, 00:15

Expert Reply

Asad wrote:

Quote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

Hello experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, AaronPond, GMATinsight, JeffTargetTestPrep, ccooley
Are the points Exactly in (3,0) and (0,2)?
Thanks__

May be, may be not but it is the only logical assumption going by the options. PS questions need to be solved. Diagrams in PS are drawn to scale. Going by the options, I know that the points are not (2.99, 0) and (0, 2.02); they must be (3, 0) and (0, 2), so why to worry.

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Re: In the coordinate system above, which of the following is the equation [#permalink]

29 Apr 2020, 14:21

Walkabout wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

Well ofcourse there is ambiguity in the following case i.e if the line is indeed passing through the points (3,0) and (0,2)

Hence i tried to negate the other equations.

A. 2x - 3y = 6
3y = 2x-6 (Y intercept is positive, hence eq cannot be true)

C. 3x + 2y = 6
2y = -3x +6
y= -3/2x + 3 (So the Y intercept is 3 and in that case the X intercept would be 2 (from m) however from the figure we see that x intercept is not on 2 but >2

D. 2x - 3y = -6
3y = 2x + 6
y = 2/3x + 3 (Cannot be true since the slope is negative as per the diagram)

E.3x -2y = -6
2y = -3x - 6 (Cannot be true since the Y intercept is positive)

Hence the answer is B

B

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Re: In the coordinate system above, which of the following is the equation [#permalink]

05 May 2020, 07:08

Looking at the diagram, we can see that the line passes through (3,0) & (0,2)
So the slope is (0-2)/(3-0)= -2/3
From A we have 3y=2x-6 so slope is 2/3 not the line
From B we have 3y=-2x+6
So y=-(2/3)x+6/3
Same slope.
In this line y=-(2/3)x+2, if we substitute 0 for x we get the y intercept as 2 which is what the line shows
Hence B

Posted from my mobile device

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Re: In the coordinate system above, which of the following is the equation [#permalink]

06 Jul 2020, 10:34

[quote="Walkabout"]

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

The two points are (0,2) and (3,0). Slope =0-2/3-0=-2/3.

We are looking for a -ve slope therefore need to choose options with positive values so that algebra works out.
(B) 2x+3y=6
3y=6-2x
y=6/3-2x/3
y=-2x/3+6/3
y=-2x/3+2

The slope of the equation will be coefficient of x, therefore -2/3.

B

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Re: In the coordinate system above, which of the following is the equation [#permalink]

15 Sep 2020, 13:20

GMATinsight wrote:

Asad wrote:

Quote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

Hello experts,
GMATinsight,
Are the points Exactly in (3,0) and (0,2)?
Thanks__

HI Asad

Since the question wants to take the reference from the figure so YES we need to interpret that the points on X and Y axis are (3,0) and (0,2). But you can answer the question without taking them exactly (3,0) and (0,2)

Look at it this way. The Line shown in figure is a Downward sloping line i.e. it has NEGATIVE SLOPE

As per the general equation of line which is y = mx+c, Options A, D and E have Positive slope hence these options are OUT

Slope in Option B = -2/3
Slope in Option C = -3/2

Now, the figure clearly depicts that absolute value of X intercept is bigger than the same for Y-intercept whereas Slope = Y intercept/X intercept

i.e. Absolute value of slope must be LESS Than 1 hence Option B is correct and Option C is out

I hope this explain!

Brilliant, just what I was looking for.. thank you

Posted from my mobile device

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Re: In the coordinate system above, which of the following is the equation [#permalink]

06 Jan 2021, 05:28

Expert Reply

As we can see that the angle made by the line with positive direction of x axis is obtuse, hence the slope of the line is Negative.

Answer Options A, D, E are eliminated, as these lines have positive slope.

Answer option B: 2x + 3y = 6. putting y = 0, we get x-intercept = 3. Possible.

Answer option C: 3x+2y = 6. putting y = 0, we get x-intercept = 2. NOT Possible, as it is clear from the figure provided, that x intercept is more than 2.

Answer is B

Walkabout wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

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Re: In the coordinate system above, which of the following is the equation [#permalink]

10 Jan 2021, 11:55

Top Contributor

Walkabout wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

The two points of line l are (0,2) and (3,0)

The slope \(= \frac{2-0}{0-3}=-\frac{2}{3}\)

\(∴ y=-\frac{2}{3}x\)

\(⇒3y=-2x\)

\(⇒ 2x+3y=0\)

B is the answer.

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Re: In the coordinate system above, which of the following is the equation [#permalink]

07 Feb 2022, 01:25

GMATBusters wrote:

As we can see that the angle made by the line with positive direction of x axis is obtuse, hence the slope of the line is Negative.

Answer Options A, D, E are eliminated, as these lines have positive slope.

Answer option B: 2x + 3y = 6. putting y = 0, we get x-intercept = 3. Possible.

Answer option C: 3x+2y = 6. putting y = 0, we get x-intercept = 2. NOT Possible, as it is clear from the figure provided, that x intercept is more than 2.

Answer is B

Walkabout wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

GMATBusters I just want to confirm if I understood your method.

Slope (m) = - x coefficient / y coefficient. So in (A) we have -2/-3 and hence +ve slope so we eliminate right? When we are considering the y coefficient we need to consider -3 and not just 3 right?

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Re: In the coordinate system above, which of the following is the equation [#permalink]

08 Feb 2022, 06:23

Expert Reply

I feel by this "Slope (m) = - x coefficient / y coefficient." : you are converting y = mx +c.
it is as per the equation, do NOT change the sign .

PS:
Do not remember "Slope (m) = - x coefficient / y coefficient." as it is incomplete :
Slope (m) = - x coefficient / y coefficient, when both x and y terms are on same side of equation : 2x+3y = 7
Slope (m) = x coefficient / y coefficient, when both x and y terms are on opposite side of equation : 2x=3y + 7

Hoozan wrote:

GMATBusters wrote:

As we can see that the angle made by the line with positive direction of x axis is obtuse, hence the slope of the line is Negative.

Answer Options A, D, E are eliminated, as these lines have positive slope.

Answer option B: 2x + 3y = 6. putting y = 0, we get x-intercept = 3. Possible.

Answer option C: 3x+2y = 6. putting y = 0, we get x-intercept = 2. NOT Possible, as it is clear from the figure provided, that x intercept is more than 2.

Answer is B

Walkabout wrote:

In the coordinate system above, which of the following is the equation of line l ?

(A) 2x - 3y = 6
(B) 2x + 3y = 6
(C) 3x + 2y = 6
(D) 2x - 3y = -6
(E) 3x - 2y = -6

Show Spoiler

Attachment:

Line L.png

GMATBusters I just want to confirm if I understood your method.

Slope (m) = - x coefficient / y coefficient. So in (A) we have -2/-3 and hence +ve slope so we eliminate right? When we are considering the y coefficient we need to consider -3 and not just 3 right?

Posted from my mobile device

D

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Re: In the coordinate system above, which of the following is the equation [#permalink]

08 Feb 2022, 21:55

GMATBusters wrote:

I feel by this "Slope (m) = - x coefficient / y coefficient." : you are converting y = mx +c.
it is as per the equation, do NOT change the sign .

PS:
Do not remember "Slope (m) = - x coefficient / y coefficient." as it is incomplete :
Slope (m) = - x coefficient / y coefficient, when both x and y terms are on same side of equation : 2x+3y = 7
Slope (m) = x coefficient / y coefficient, when both x and y terms are on opposite side of equation : 2x=3y + 7

Yes, when I say (m) = - coefficient of x / coefficient of y I am assuming the equation 2x + 3y = 7.

Thanks for making the difference in the two types of equations clear

B

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Re: In the coordinate system above, which of the following is the equation [#permalink]

17 Nov 2023, 10:42

schen wrote:

Just a different way of approaching the problem...
since we know the y-intercept is -c/b when the equation is given in the form ax+by +c =0.. simply use what's on the right side of the equation (it'll turn negative when moved to the left) and divide by b.

This way doesn't work, please do not use this method, in this case, D would qualify as well.

gmatclubot

Re: In the coordinate system above, which of the following is the equation [#permalink]

17 Nov 2023, 10:42

GMAT Problem Solving (PS) Questions

In the coordinate system above, which of the following is the equation