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505-555 Level|   Coordinate Geometry|                                    
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In the coordinate system above, which of the following is the equation 12 Nov 2019, 12:58
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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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In the coordinate system above, which of the following is the equation 15 Nov 2019, 23:26
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Bunuel

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.
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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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In the coordinate system above, which of the following is the equation 21 Apr 2020, 18:34
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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
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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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In the coordinate system above, which of the following is the equation 21 Apr 2020, 22:07
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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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Hello Asad,

I agree with you that the diagram is not complete in terms of telling you where the line cuts the x and the y axis. So, your difficulty is understandable.

However, the diagram is just one component of this PS question. In a PS question, remember that the answer options are as important a component of the question as any other. As such, if you do not take clues from the answer options, you may be at a loss in questions like these.

A quick glance at the answer options should tell you that the intercepts are 3 and 2. There aren’t any other numbers other than these two, in any of the options. That’s a clear clue. Additionally, observe the diagram carefully:

On the x-axis, the diagram shows 2 divisions clearly and then shows the line cutting the x-axis. These three divisions are equally spaced as well. Having looked at the answer options, you can now conclusively say that the x-intercept should be 3.

Similarly, on the y-axis, the diagram shows 2 equally spaced divisions. Again, it’s not hard to conclude that the y-intercept should be 2.

Using the intercept form of the equation of a line i.e. \(\frac{x}{a}\) + \(\frac{y}{b}\) = 1, we have,

\(\frac{x}{3}\) + \(\frac{y}{2}\) = 1, which simplifies to 2x + 3y = 6.

Hope that answers your question!
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In the coordinate system above, which of the following is the equation 21 Apr 2020, 23:32
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Asad
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__
Show more

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! :)
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In the coordinate system above, which of the following is the equation 23 Apr 2020, 00:15
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Asad
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)?
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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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In the coordinate system above, which of the following is the equation 29 Apr 2020, 14:21
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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

Show Spoiler
Attachment:
Line L.png
Show more

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
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In the coordinate system above, which of the following is the equation 05 May 2020, 07:08
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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

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In the coordinate system above, which of the following is the equation 06 Jul 2020, 10:34
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[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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In the coordinate system above, which of the following is the equation 15 Sep 2020, 13:20
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GMATinsight
Asad
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! :)
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Brilliant, just what I was looking for.. thank you

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In the coordinate system above, which of the following is the equation 06 Jan 2021, 05:28
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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

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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In the coordinate system above, which of the following is the equation 10 Jan 2021, 11:55
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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

Show Spoiler
Attachment:
Line L.png
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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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In the coordinate system above, which of the following is the equation 07 Feb 2022, 01:25
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GMATBusters
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

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
Show more

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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In the coordinate system above, which of the following is the equation 08 Feb 2022, 06:23
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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
GMATBusters
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

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?
Show more

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In the coordinate system above, which of the following is the equation 08 Feb 2022, 21:55
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GMATBusters
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
Show more


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 :)
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In the coordinate system above, which of the following is the equation 01 Jun 2022, 07:03
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In the coordinate system above, which of the following is the equation 17 Nov 2023, 10:42
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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.
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This way doesn't work, please do not use this method, in this case, D would qualify as well.
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In the coordinate system above, which of the following is the equation 26 Mar 2025, 03:43
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