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In the xycoordinate plane, which of the following points must lie on [#permalink]
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16 Oct 2015, 07:32
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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16 Oct 2015, 07:43
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Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. We're looking for a set of coordinates that are not affected by the value of k. Notice that, in answer choice B (0,2), the xcoordinate is 0 and y = 2 So, if we plug x = 0 and y = 2 into the equation kx + 3y = 6, we get k( 0) + 3(2) = 6 Notice that, since x = 0, the value of k is irrelevant. So, ( 0, 2) will ALWAYS be a point on the line kx + 3y = 6 Answer: B Cheers, Brent
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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16 Oct 2015, 08:00
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Here for any value of k points should lie on the line means we can substitute any value for k so let k =1,2 then the equations will be L x+3y=6 (1) and 2x+3y=6 (2) Now after solving the simultaneous equations above we would get the values for x as 0 and y as 2. Hence (0,2) Option B



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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16 Oct 2015, 08:20
kx + 3y = 6 Answer B (0,2) K * 0 + 3 * 2 = 6
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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17 Oct 2015, 05:00
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Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Kx+3y = 6 since we need to make the coordinates independent of K  Lets put x = 0. 3y = 6 so y =2 We get a point (0,2) so B.
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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17 Oct 2015, 06:52
Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Property : The points must satisfy the given equation of line in order to lie on the linekx + 3y = 6 will be satisfied only when x coordinate is zero as k is unknown variable. Hence, Without checking any option the correct answer must have xcpordinate zero which is the case in option B Answer: Option B
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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13 Feb 2016, 16:52
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Although I took >3 mins to solve this the first time, after some thinking, I could see one nice takeaway from this question  for any line y=mx+c, the y intercept  c  is a point that will always exist on the line, independent of x or slope m. In this case, the yintercept is (0,2). So with any value of k or x, (0,2) will always be a point on this line and therefore is the correct answer. Similarly, let's say the equation of the line was 6x + ky = 6, try thinking what will be a point that will always lie on this line for every possible value of k? (1,0), i.e. the xintercept HTH



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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13 Feb 2016, 17:17
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We're looking for a set of coordinates that are not affected by the value of k. in answer choice B (0,2), the xcoordinate is 0 and y = 2 So, if we plug x = 0 and y = 2 into the equation kx + 3y = 6, we get k(0) + 3(2) = 6 Notice that, since x = 0, the value of k is irrelevant. So, (0, 2) will ALWAYS be a point on the line kx + 3y = 6 so my answer is b
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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10 May 2016, 18:24
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Attached is a visual that should help.
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In the xycoordinate plane, which of the following points must lie on [#permalink]
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11 May 2016, 02:13
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Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Yes all the above methods are correct but we are forgetting one basic fact. Form eqn of line we have y = k/3*x+2. From eqn we can clearly see that the y intercept of line = 2. So no matter what slope the line has intercept of yaxis will always be 2. So point (0,2) will always be on the line.Ans is B



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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17 Nov 2016, 09:47
Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Here, my job is to remove 'K' from the equation. The equation says: kx + 3y = 6 If i want to remove 'k' from the equation, then i must be put x=0. So, B (0,2) makes sense. kx + 3y = 6 > k*0+3*2=6 > 0+6=6 > 6=6, whic is always correct So, the correct answer is B.
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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17 Nov 2016, 10:21
I did this by substituting each of the values. For (0,2) any value of k still gives kx =0. therefore (0,2)
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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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22 Jan 2017, 10:35
I changed the given equation to the slope yintercept form;
y=(k/3)x+2,
Since in this form, the constant is always the Yintercept i expect the answer to be (something,2). Thus the answer is B. Is this correct?



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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03 Jun 2017, 01:17
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Put the given equation in y=mx+b form, as already indicated above. Now test the answers till you find the match that LHS = RHS, only option B yields 2=2, in which also k gets irrelevant as you multiply k by 0!



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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05 Nov 2017, 16:37
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Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. 1. The point must lie on the line kx + 3y = 6 2. Every possible value of K must satisfy So when will every possible value of K satisfy this equation? When the value of K does not impact the solution and this will happen when x = 0. Only Option B has X = 0. Also, because the point must lie on the line, y has to be equal to 2 when x = 0.



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In the xycoordinate plane, which of the following points must lie on [#permalink]
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14 Feb 2018, 11:40
Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Hi niks18 here is my solution which i dont understand myself so we have: \(kx3y = 6\) now i will rewrite in the form of yintercept formula \(y = mx+b\) \(3y = 6kx\) \(3y = kx+6\) \(y = \frac{kx}{3}+ 2\) I have no idea what kx is here i got stuck, how to answer this question gimme a hint



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Re: In the xycoordinate plane, which of the following points must lie on [#permalink]
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14 Feb 2018, 11:59
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dave13 wrote: Bunuel wrote: In the xycoordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?
(A) (1,1) (B) (0,2) (C) (2,0) (D) (3,6) (E) (6,3)
Kudos for a correct solution. Hi niks18 here is my solution which i dont understand myself so we have: \(kx3y = 6\) now i will rewrite in the form of yintercept formula \(y = mx+b\) \(3y = 6kx\) \(3y = kx+6\) \(y = \frac{kx}{3}+ 2\) I have no idea what kx is here i got stuck, how to answer this question gimme a hint Hi dave13Read the question carefully. It says “something” is true for any value of k. That is you need to make k irrelevant here. So how will that be possible? This is possible in ONLY one way when you multiply k by 0 because any number multiplied by 0 is 0. In this question you have kx. So do you have any option that makes x=0?, if yes then that will be your answer. What you did is you found out the slope of the straight line “m” which comes out to be k/3. All these workings are not required if you understood the above method. Posted from my mobile device




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