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In the xycoordinate plane, which of the following points must lie on
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16 Oct 2015, 07:32
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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) PS02947
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Re: In the xycoordinate plane, which of the following points must lie on
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16 Oct 2015, 07:43
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
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16 Oct 2015, 08:00
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
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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
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17 Oct 2015, 05:00
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
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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
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13 Feb 2016, 16:52
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
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13 Feb 2016, 17:17
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
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10 May 2016, 18:24
Attached is a visual that should help.
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Screen Shot 20160510 at 5.53.01 PM.png [ 80.64 KiB  Viewed 24059 times ]



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Re: In the xycoordinate plane, which of the following points must lie on
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11 May 2016, 02:13
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
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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
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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
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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
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03 Jun 2017, 01:17
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
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05 Nov 2017, 16:37
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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Re: In the xycoordinate plane, which of the following points must lie on
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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
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14 Feb 2018, 11:59
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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Re: In the xycoordinate plane, which of the following points must lie on
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22 Mar 2018, 05:20
Bunuel VeritasPrepKarishma. Could you please show a detailed approach and the theory underneath this problem? Thanks.



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Re: In the xycoordinate plane, which of the following points must lie on
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22 Mar 2018, 05:49
sadikabid27 wrote: Bunuel VeritasPrepKarishma. Could you please show a detailed approach and the theory underneath this problem? Thanks. The first thing I do here is put it in the form of y = mx + c because that tells me a lot about the line represented by the equation. y = kx/3 + 2 Slope = k/3 and y intercept is 2 (which means the line passes through (0, 2)). So depending on the value of k, we will draw a line through the point (0, 2). For every value of k means no matter what the slope is, the line must pass through the point we need. We know only one such point (0, 2). Do we have it in the options? Yes. Answer (B)
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Re: In the xycoordinate plane, which of the following points must lie on
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20 Aug 2018, 08:01
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. Let's rewrite the equation in slope yintercept form y = mx + b, where m is the slope of the line and b is the line's yinterceptTake: kx + 3y = 6 Subtract kx from both sides: 3y = 6  kx Divide both sides by 3 to get: y = 2  kx/3 Rewrite as: y = (k/3)x + 2So, the slope of the line is k/3 and the yintercept is 2If the yintercept is 2, then the line must pass through the point (0, 2) Answer: B Cheers, Brent
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Re: In the xycoordinate plane, which of the following points must lie on
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