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In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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03 May 2013, 18:43
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78% (01:45) correct 22% (02:22) wrong based on 213 sessions
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In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y = (A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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04 May 2013, 04:46
manishuol wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12 Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x. Thus: (x, 1)=( 2, 1) and (10, y) = (10, 5) > x+y=2+5=7. Answer: B.
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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17 Nov 2013, 22:41
avohden wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12
As both the points are on the same line, and the line passes through the origin with a positive slope, \(\frac{10}{x0} = \frac{1}{2}\) and \(\frac{y0}{100} = \frac{1}{2}\) Hence, x=2 and y=5 Thus, x+y = 7 B. IMO more like 550.
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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04 May 2013, 07:52
We know the equation of any line is y=mx+c Where m = slope and c = y intercept (point where line crosses y axis) Since line passes thru origin then y intercept (i.e. C) must be zero we also know m = slope = 1/2 so the equation becomes y=\(\frac{x}{2}\) we are given two points that are on line (x,1) (10,y) Plug second point (10,y) in to the equation y=\(\frac{10}{2}\) > y=5 Plug First point (x,1) in to the equation 1=\(\frac{x}{2}\) > x=2 x+y = 7 Choice B Regards, Narenn
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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04 May 2013, 11:02
manishuol wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12 Equation of a line passing through origin and having a slope m is given by \(y = mx\) Hence the equation of the given line is \(y = 0.5 * x\) This gives the values of x and y as 2 and 5 respectively. Hence x + y = 7 Correct Answer is B



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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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21 Oct 2013, 11:18
My approach was to apply the rise/run=slope rule so, y1/10x = 1/2 2y2=10x 2y+x=12, substitute with one of the given points (x,1) 2(1) +x=12, x=10, y=1, x+y=11 can someone please tell me why this approach doesn't work?
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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21 Oct 2013, 11:40
SaraLotfy wrote: My approach was to apply the rise/run=slope rule
so,
y1/10x = 1/2 2y2=10x 2y+x=12, substitute with one of the given points (x,1) 2(1) +x=12, x=10, y=1, x+y=11
can someone please tell me why this approach doesn't work? IMO what you have obtained (2y+x=12) is the algebraic equation, but it is not the equation of a line. Equation of line is described as y=mx+c > where 'm' is the slope of a line and 'c' is the 'y' intercept. Per the equation 2y+x=12 \(m=slope=\frac{1}{2}\) (which is not correct. The slope is \(\frac{1}{2}\)) c=y intercept = 6 (This is also not correct. We know that line is passing thru origin, so its y intercept (the y value of point where line crosses 'y' axis) must be zero.
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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20 Nov 2013, 17:43
Answer: B We're given the slope of a line and one point on the line (the origin: 0,0). From this, we can determine every other point on the line. The most direct way to find x and y involves solving for each individually.
We know that slope (1/2, in this case), is equal to the change in y divided by the change in x. Since we know that the line passes through (0,0) and (x,1), we can solve as follows:
1/2 = (1 – 0)/(x – 0) 1/2 = 1/x x = 2
Use the same approach to solve for y:
1/2 = (y – 0)/(10 – 0) 1/2 = y/10 y = 5
Thus, x + y = 2 + 5 = 7, choice (B).



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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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28 Dec 2013, 09:16
mau5 wrote: avohden wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12
As both the points are on the same line, and the line passes through the origin with a positive slope, \(\frac{10}{x0} = \frac{1}{2}\) and \(\frac{y0}{100} = \frac{1}{2}\) Hence, x=2 and y=5 Thus, x+y = 7 B. IMO more like 550. One can only check the coordiantes and solve See, we are given that y = 1/2x So first coordinate since y =1 then x = 2 Second coordinate since x = 1= then y=5 So add em up 2+5 = 7 B Hope its clear Cheers J



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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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26 May 2015, 21:52
Hi All, This question has a great "brute force" element to it. Since we know that the line passes through the Origin (0,0) and has a slope of 1/2, we can "map out" as many coordinates as we need to to answer the given question. Since the slope is 1/2, for every increase of 2 in the Xcoordinate we have an increase of 1 in the Ycoordinate: (0,0) (2,1) (4,2) (6,3) (8,4) (10, 5) We're told that (X,1) and (10,Y) are on the line. We're asked for the value of X+Y.... From our list of coordinates, we can see that X = 2 and Y = 5... X+Y = 2+5 = 7 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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27 May 2016, 07:29
Slope m = (y2  y1) / (x2  x1) formula equation there are three points on the line (0,0) , (x,1) and (10,y). given m = 1/2. first take (0,0) , (x,1) and m=1/2 and put these in formula equation and we get 1/2 = 10 / x0 hence x=2 first take (0,0) , (10,y) and m=1/2 and put these in formula equation and we get 1/2 = y0 / 100 hence y=5 x+y = 5+2 = 7.
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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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14 Feb 2018, 12:52
manishuol wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12 Hi niks18 please let me know if my solution/ approach is correct ? \(\frac{1y}{x10}=\frac{1}{2}\) cross multiply \(22y = x10\) \(x102+2y\) \(x+2y12 = 0\) \(2y= 12x\) \(y = \frac{x}{2}+ 6\) now since I know that slop is \(1/2\) hence x = 1 and y intercept is 6 so x+y = 1+6 = 7 Answer: 7 < many thanks!



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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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15 Feb 2018, 03:14
dave13 wrote: manishuol wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12 Hi niks18 please let me know if my solution/ approach is correct ? \(\frac{1y}{x10}=\frac{1}{2}\) cross multiply \(22y = x10\) \(x102+2y\) \(x+2y12 = 0\) \(2y= 12x\) \( y = \frac{x}{2}+ 6\)
now since I know that slop is \(1/2\) hence x = 1 and y intercept is 6 so x+y = 1+6 = 7 Answer: 7 < :) many thanks! :) Hi dave13, what you have done is used the formula to find slope and converted it to an algebraic equation which does not represent the equation of line. equation of line is \(y=mx+c\), where \(m\) is slope of the line as per your equation \(y=\frac{1}{2}x+6\), so here slope, \(m=\frac{1}{2}\) which is incorrect. We know that the line passes through the origin so our equation should be \(y=\frac{1}{2}x+c\) and at origin we have (0,0) so \(0=\frac{1}{2}*0+c => c=0\) i.e yintercept is 0 (as per your equation y intercept is 6 which is incorrect). If a line passes through origin it will not cut yaxis and hence there will be no intercept. Hence equation of line will be \(y=\frac{1}{2}x\) now at (x,1) we will have \(1=\frac{1}{2}x=>x=2\) and at (10,y) we will have \(y=\frac{1}{2}*10 =>y=5\) Hence \(x+y=2+5=7\) There is an alternate method as well using only the formula to find slope. This method is also explained in earlier posts.



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Re: In the coordinate plane, points (x, 1) and (10, y) are on line k. If
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20 Feb 2018, 17:14
manishuol wrote: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5 (B) 7 (C) 8 (D) 11 (E) 12 Since the slope m of the line is ½ and the line passes through (x, 1) and the origin (0,0), we use the slope formula m = (y1  y2)/(x1  x2) and we have: (1  0)/(x  0) = 1/2 1/x = 1/2 x = 2 Similarly, using the points (10, y) and the origin, we can create the equation: (y  0)/(10  0) = 1/2 y/10 = 1/2 y = 5 Thus, x + y = 2 + 5 = 7. Answer: B
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