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# ln the coordinate plane, line k passes through the origin

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ln the coordinate plane, line k passes through the origin [#permalink]

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10 Oct 2011, 08:30
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ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

[Reveal] Spoiler: My Take
i used the method y2-y1/x1-x2 =2

4-y/x-3 =2

As line passes through origin y=2x
Upon solving both the equation i get x+y=7.5

OOps some different method required.

Guys is this the trick in Coordinate geometry that we generally have to put points in line and chk.instead of making equations with the points given.

Pls comment

@Fluke ---i searched this question but didn't found.
[Reveal] Spoiler: OA

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10 Oct 2011, 08:55
5
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I think we have to go with general equation of line with two points.

y-y1/y2-y1 = x-x1/x2-x1

And substituting the values:

y-4 = 2(x-x1) => x1 =2 (as (0,0) is on the line).
4-y1=2(x-3) => y1= 6 (as (0,0) is on the line).

x+y = 8; Ans:C.

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Re: OG PS: Line k with slope 2 [#permalink]

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10 Oct 2011, 09:05
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GMATD11 wrote:
ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Sol:
y=mx+c
m=Slope=2
c=intersection on y-axis=0
y=2x

The line passes through (3,y)
y=2*3=6

The line also passes through (x,4)
4=2*x;
x=2;

x+y=2+6=8

Ans: "C"
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Re: OG PS: Line k with slope 2 [#permalink]

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10 Oct 2011, 10:07
14
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Expert's post
15
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GMATD11 wrote:
ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

[Reveal] Spoiler: My Take
i used the method y2-y1/x1-x2 =2

4-y/x-3 =2

As line passes through origin y=2x
Upon solving both the equation i get x+y=7.5

OOps some different method required.

Guys is this the trick in Coordinate geometry that we generally have to put points in line and chk.instead of making equations with the points given.

Pls comment

@Fluke ---i searched this question but didn't found.

To find the line k, knowing a point through which it passes and the line's slope is sufficient.
Since it passes through origin and has slope 2, this is what it will look like:
Attachment:

Ques6.jpg [ 4.9 KiB | Viewed 18719 times ]

What is the meaning of slope? It means for every increase of 1 unit in x coordinate, y coordinate increases by 2 units. When x coordinate increases by 3 units (from the point (0,0)), y coordinate increases by 6 units. Hence the line passes through (3, 6). y must be 6.
When y coordinate increases by 4 units (from (0,0)), x coordinate must have increased by 2 units. The line must pass through (2, 4). x must be 2.
x+y = 2+6 = 8
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17808 [14], given: 235 Director Joined: 01 Feb 2011 Posts: 725 Kudos [?]: 146 [2], given: 42 Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 10 Oct 2011, 19:57 2 This post received KUDOS 1 This post was BOOKMARKED x and y in those points (x,4) and y in (3,y) can be confusing . you ran into this situation because you are trying to solve two equations y = 2x and 2x+y=10. Thats not correct x and y in 2x+y = 10 refer to x in (x,4) and y in (3,y) and belong to two different points where as y=2x is the generic equation . here x and y belong to same point. to avoid confusion i would say you can replace the points as (3,p) and (q,4) and rephrase the question as p+q=? equation of the line passing through origin and slope 2 => y = 2x then you can compare slopes slope of (3,p) and (0,0) = 2 => p/3 = 2 => p=6 slope of (q,4) and (0,0) = 2 => 4/q = 2 => q = 2 => p+q = 8 GMATD11 wrote: ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y = (A) 3.5 (B) 7 (C) 8 (D) 10 (E) 14 [Reveal] Spoiler: My Take i used the method y2-y1/x1-x2 =2 4-y/x-3 =2 As line passes through origin y=2x Upon solving both the equation i get x+y=7.5 OOps some different method required. Guys is this the trick in Coordinate geometry that we generally have to put points in line and chk.instead of making equations with the points given. Pls comment @Fluke ---i searched this question but didn't found. Kudos [?]: 146 [2], given: 42 Manager Joined: 20 Aug 2011 Posts: 144 Kudos [?]: 108 [0], given: 0 Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 10 Oct 2011, 22:44 y=2x is the req. line hence y=6 & x=2 so x+y=8 C _________________ Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general. Kudos [?]: 108 [0], given: 0 Manager Joined: 16 Dec 2009 Posts: 74 Kudos [?]: 41 [3], given: 11 GMAT 1: 680 Q49 V33 WE: Information Technology (Commercial Banking) Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 24 Nov 2011, 22:58 3 This post received KUDOS Points (3,y) and origin lies on the same line and have a slope of 2. So (y-0)/(3-0)=2 or y=6 Points (x,4) and origin lies on the same line and have a slope of 2. So (4-0)/(x-0)=2 or x=2 So x+y=8 .. Answer choice (C) _________________ If Electricity comes from Electrons , Does Morality come from Morons ?? If you find my post useful ... then please give me kudos ...... h(n) defined as product of even integers from 2 to n Number N divided by D leaves remainder R Ultimate list of MBA scholarships for international applicants Kudos [?]: 41 [3], given: 11 Intern Joined: 16 Jan 2012 Posts: 4 Kudos [?]: [0], given: 0 Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 25 Feb 2012, 15:24 I got this wrong and I cant figure what is wrong with my approach (y2-y1)/(x2-x1)=m (slope) so we have 2 points x,4 and 3,y so we get the eq (y-4)/(3-x)=2. simplifying this we get : y= 10-2x so I get the value of y=4 and x=3 and hence the sum 7. Why is this wrong? Kudos [?]: [0], given: 0 Math Expert Joined: 02 Sep 2009 Posts: 42257 Kudos [?]: 132742 [5], given: 12360 Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 25 Feb 2012, 15:50 5 This post received KUDOS Expert's post 1 This post was BOOKMARKED Ashamock wrote: I got this wrong and I cant figure what is wrong with my approach (y2-y1)/(x2-x1)=m (slope) so we have 2 points x,4 and 3,y so we get the eq (y-4)/(3-x)=2. simplifying this we get : y= 10-2x so I get the value of y=4 and x=3 and hence the sum 7. Why is this wrong? Welcome to GMAT Club. Below is an answer to your question: There are infinitely many values of x and y possible to satisfy y=10-2x. For any value of x there exist some y for which y=10-2x holds true (and vise versa). For example: x=1, y=8 or x=2, y=6, or x=0.5, y=9, ... Also notice that you won't be able to find the value of x+y without one more piece of information given in the stem, namely information saying that line k passes through the origin. There are several approaches discussed above how to handle this problem, I'd offer one more. ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y = (A) 3.5 (B) 7 (C) 8 (D) 10 (E) 14 Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line) then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get: For point (3,y) --> $$y=2*3=6$$; For point (x,4) --> $$4=2x$$ --> $$x=2$$; $$x+y=8$$. Answer: C. Check Coordinate Geometry chapter of Math Book for more on this subject: math-coordinate-geometry-87652.html Hope it helps. _________________ Kudos [?]: 132742 [5], given: 12360 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7738 Kudos [?]: 17808 [2], given: 235 Location: Pune, India Re: OG PS: Line k with slope 2 [#permalink] ### Show Tags 27 Feb 2012, 04:53 2 This post received KUDOS Expert's post Ashamock wrote: I got this wrong and I cant figure what is wrong with my approach (y2-y1)/(x2-x1)=m (slope) so we have 2 points x,4 and 3,y so we get the eq (y-4)/(3-x)=2. simplifying this we get : y= 10-2x so I get the value of y=4 and x=3 and hence the sum 7. Why is this wrong? Let me point out one thing I noticed: How did you get y = 4 and x = 3? The equation you get is y= 10-2x. Mind you, here y = y2 and x = x1 i.e. they are y and x co-ordinates of different points. y = 10 - 2x can give you the value of y + 2x i.e. equal to 10 but how do you get the value of (y+x)? You can go from here and find the answer if you consider the info that the line passes through the center. Say, the 2 points on the line that you are considering are (0, 0) and (x, 4) (y2-y1)/(x2-x1)=m (4 - 0)/(x - 0) = 2 x = 2 Now you can plug x = 2 in y = 10 - 2x to get y = 6 Their sum 2+6 = 8 Hope you understand that these x and y stand for particular values. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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31 Mar 2012, 05:58
I made the same mistake as well.

(y2-y1)/(x2-x1)=m (slope)
so we have 2 points
x,4 and 3,y
so we get the eq
(y-4)/(3-x)=2.

simplifying this we get :
y= 10-2x

so I get the value of y=4 and x=3 and hence the sum 7.

Can someone explain why this is wrong. I couldn't understand.
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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31 Mar 2012, 06:16
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Expert's post
I made the same mistake as well.

(y2-y1)/(x2-x1)=m (slope)
so we have 2 points
x,4 and 3,y
so we get the eq
(y-4)/(3-x)=2.

simplifying this we get :
y= 10-2x

so I get the value of y=4 and x=3 and hence the sum 7.

Can someone explain why this is wrong. I couldn't understand.

This two posts address the same exact issue:
ln-the-coordinate-plane-line-k-passes-through-the-origin-121790.html#p1049905
ln-the-coordinate-plane-line-k-passes-through-the-origin-121790.html#p1050438
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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08 Jul 2013, 01:10
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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04 Sep 2013, 02:37
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

Y = mx + c where m=slope and c = Y intercept

We have that m = slope = 2 AND c = Y Intercept = 0 (We know like passes thru origin

Hence The equation of line is y = (2)x + 0 ------> y = 2x

point (3,y) ------> y = 6
point (x,4) -------> 4 = 2x ------> x = 2

Hence x + y 8
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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19 Oct 2014, 07:11
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ln the coordinate plane, line k passes through the origin [#permalink]

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13 Sep 2015, 13:41
Bunuel wrote:
Ashamock wrote:
I got this wrong and I cant figure what is wrong with my approach
(y2-y1)/(x2-x1)=m (slope)
so we have 2 points
x,4 and 3,y
so we get the eq
(y-4)/(3-x)=2.

simplifying this we get :
y= 10-2x

so I get the value of y=4 and x=3 and hence the sum 7.

Why is this wrong?

There are infinitely many values of x and y possible to satisfy y=10-2x. For any value of x there exist some y for which y=10-2x holds true (and vise versa). For example: x=1, y=8 or x=2, y=6, or x=0.5, y=9, ... Also notice that you won't be able to find the value of x+y without one more piece of information given in the stem, namely information saying that line k passes through the origin.

There are several approaches discussed above how to handle this problem, I'd offer one more.

ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line) then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get:
For point (3,y) --> $$y=2*3=6$$;
For point (x,4) --> $$4=2x$$ --> $$x=2$$;

$$x+y=8$$.

Check Coordinate Geometry chapter of Math Book for more on this subject: math-coordinate-geometry-87652.html

Hope it helps.

I still don'Tget why we canot use the slope formula here ...? y= 10-2x
The slope formula regards always 2 different points.. if we have 2 points we can build an equation of the line..

Using (0,0 and (3,y) we get the right answer, BUT using 3y and x,4 not
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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14 Sep 2015, 05:25
BrainLab wrote:
Bunuel wrote:
Ashamock wrote:
I got this wrong and I cant figure what is wrong with my approach
(y2-y1)/(x2-x1)=m (slope)
so we have 2 points
x,4 and 3,y
so we get the eq
(y-4)/(3-x)=2.

simplifying this we get :
y= 10-2x

so I get the value of y=4 and x=3 and hence the sum 7.

Why is this wrong?

There are infinitely many values of x and y possible to satisfy y=10-2x. For any value of x there exist some y for which y=10-2x holds true (and vise versa). For example: x=1, y=8 or x=2, y=6, or x=0.5, y=9, ... Also notice that you won't be able to find the value of x+y without one more piece of information given in the stem, namely information saying that line k passes through the origin.

There are several approaches discussed above how to handle this problem, I'd offer one more.

ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line) then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get:
For point (3,y) --> $$y=2*3=6$$;
For point (x,4) --> $$4=2x$$ --> $$x=2$$;

$$x+y=8$$.

Check Coordinate Geometry chapter of Math Book for more on this subject: math-coordinate-geometry-87652.html

Hope it helps.

I still don'Tget why we canot use the slope formula here ...? y= 10-2x
The slope formula regards always 2 different points.. if we have 2 points we can build an equation of the line..

Using (0,0 and (3,y) we get the right answer, BUT using 3y and x,4 not

Have you checked this post: ln-the-coordinate-plane-line-k-passes-through-the-origin-121790.html#p1050438
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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14 Sep 2015, 06:00
Why is this wrong?[/quote]

There are infinitely many values of x and y possible to satisfy y=10-2x. For any value of x there exist some y for which y=10-2x holds true (and vise versa). For example: x=1, y=8 or x=2, y=6, or x=0.5, y=9, ... Also notice that you won't be able to find the value of x+y without one more piece of information given in the stem, namely information saying that line k passes through the origin.

There are several approaches discussed above how to handle this problem, I'd offer one more.

ln the coordinate plane, line k passes through the origin and has slope 2. lf points (3,y) and (x,4) are on line k, then x+y =
(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line) then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get:
For point (3,y) --> $$y=2*3=6$$;
For point (x,4) --> $$4=2x$$ --> $$x=2$$;

$$x+y=8$$.

Check Coordinate Geometry chapter of Math Book for more on this subject: math-coordinate-geometry-87652.html

Hope it helps.[/quote]

I still don'Tget why we canot use the slope formula here ...`? y= 10-2x
The slope formula regards always 2 different points.. if we have 2 points we can build an equation of the line..

Using (0,0 and (3,y) we get the right answer, BUT using 3y and x,4 not[/quote]

Have you checked this post: ln-the-coordinate-plane-line-k-passes-through-the-origin-121790.html#p1050438[/quote]

Hi Bunuel, yes, I've already seen the reply from Karishma, but I still don't get it. What is the difference between using (3,y) & (x,4) and (3,y) & (0,0). Both points lay on the line. For exm. if we have coordinates (2,5) and (12,18) we can easily build an eyuation for this line, first finding the slope and then the y-intercept....
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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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15 May 2016, 22:01
I'm stumped!

what is wrong in the approach below?

y= 2x+c (we know that c=0). Thus,
y=2x........equation 1

next,
(4-y)/(x-3)= 2
Thus, 10= 2x+y....equation 2

From equation 1 & equation 2, I found x= 5/2 & y= 5.
Thus x+y= 7.5

I'm not understanding what is wrong in this process!

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Re: ln the coordinate plane, line k passes through the origin [#permalink]

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16 May 2016, 00:10
1
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Expert's post
kanav06 wrote:
I'm stumped!

what is wrong in the approach below?

y= 2x+c (we know that c=0). Thus,
y=2x........equation 1

next,
(4-y)/(x-3)= 2
Thus, 10= 2x+y....equation 2

From equation 1 & equation 2, I found x= 5/2 & y= 5.
Thus x+y= 7.5

I'm not understanding what is wrong in this process!

y = 2x is the equation of the line - fine.

But these two - (3,y) and (x,4) are points. Here y and x are specific co-ordinate points.

Think of them instead as points (3, a) and (b, 4). You need to find a + b.
You will get 10 = 2a + b by equating it to slope but how will you solve for a + b?

The equation of the line is y = 2x
So a = 2*3 = 6
Also, 4 = 2*b
b = 2

So a + b = 6 + 2 = 8
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Re: ln the coordinate plane, line k passes through the origin   [#permalink] 16 May 2016, 00:10

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