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

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

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New post 12 Nov 2019, 11:58
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]

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New post 15 Nov 2019, 22:26
Bunuel wrote:
Image
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]

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New post 21 Apr 2020, 17:34
Quote:
Image
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

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

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New post 21 Apr 2020, 21:07
Asad wrote:
Quote:
Image
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

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__


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

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New post 21 Apr 2020, 22:32
Asad wrote:
Quote:
Image
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

Attachment:
Line L.png

Hello experts,
GMATinsight,
Are the points Exactly in (3,0) and (0,2)?
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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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Re: In the coordinate system above, which of the following is the equation  [#permalink]

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New post 22 Apr 2020, 23:15
Asad wrote:
Quote:
Image
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

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]

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New post 29 Apr 2020, 13:21
Walkabout wrote:
Image
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

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

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New post 05 May 2020, 06:08
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

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Re: In the coordinate system above, which of the following is the equation   [#permalink] 05 May 2020, 06:08

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