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In the xy-coordinate plane, which of the following points must lie on

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In the xy-coordinate plane, which of the following points must lie on [#permalink]

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In the xy-coordinate 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)


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[Reveal] Spoiler: OA

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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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Bunuel wrote:
In the xy-coordinate 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)


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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 x-coordinate 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

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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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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 xy-coordinate plane, which of the following points must lie on [#permalink]

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New post 16 Oct 2015, 08:20
kx + 3y = 6

Answer B (0,2)
K * 0 + 3 * 2 = 6
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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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Bunuel wrote:
In the xy-coordinate 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)


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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 xy-coordinate plane, which of the following points must lie on [#permalink]

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Bunuel wrote:
In the xy-coordinate 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)


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Property : The points must satisfy the given equation of line in order to lie on the line

kx + 3y = 6 will be satisfied only when x co-ordinate is zero as k is unknown variable.

Hence, Without checking any option the correct answer must have x-cp-ordinate zero which is the case in option B

Answer: Option B
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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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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 y-intercept 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?
[Reveal] Spoiler:
(1,0), i.e. the x-intercept


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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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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 x-coordinate 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 xy-coordinate plane, which of the following points must lie on [#permalink]

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Attached is a visual that should help.
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Screen Shot 2016-05-10 at 5.53.01 PM.png
Screen Shot 2016-05-10 at 5.53.01 PM.png [ 80.64 KiB | Viewed 7015 times ]


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In the xy-coordinate plane, which of the following points must lie on [#permalink]

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Bunuel wrote:
In the xy-coordinate 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)


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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 y-axis will always be 2.
So point (0,2) will always be on the line.

Ans is B

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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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New post 17 Nov 2016, 09:47
Bunuel wrote:
In the xy-coordinate 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)


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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 xy-coordinate plane, which of the following points must lie on [#permalink]

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New post 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 xy-coordinate plane, which of the following points must lie on [#permalink]

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New post 22 Jan 2017, 10:35
I changed the given equation to the slope y-intercept form;

y=(-k/3)x+2,

Since in this form, the constant is always the Y-intercept i expect the answer to be (something,2). Thus the answer is B. Is this correct?

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Re: In the xy-coordinate plane, which of the following points must lie on [#permalink]

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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 xy-coordinate plane, which of the following points must lie on [#permalink]

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New post 05 Nov 2017, 16:37
Bunuel wrote:
In the xy-coordinate 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 xy-coordinate plane, which of the following points must lie on   [#permalink] 05 Nov 2017, 16:37
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