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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)

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 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

Re: In the xy-coordinate 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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16 Oct 2015, 08:20

kx + 3y = 6

Answer B (0,2) K * 0 + 3 * 2 = 6
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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)

Kudos for a correct solution.

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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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 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?

Re: In the xy-coordinate 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 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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Please award kudos if you like my explanation. Thanks

In the xy-coordinate 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 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.

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

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

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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)

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. _________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

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Re: In the xy-coordinate 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!

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

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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.