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

Question

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)

PS02947

BrentGMATPrepNow · Accepted Answer

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

Cheers,
Brent

m2k · Answer

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

Skywalker18 · Answer

kx + 3y = 6

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

M3sSiaH · Answer

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.

GMATinsight · Answer

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

Dienekes · Answer

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?

Show Spoiler

(1,0), i.e. the x-intercept

HTH

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 x-intercept

HTH

shakticnb · Answer

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

mcelroytutoring · Answer

Attached is a visual that should help.

wings.ap · Answer

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

sadikabid27 · Answer

Bunuel   VeritasPrepKarishma . Could you please show a detailed approach and the theory underneath this problem? Thanks.

KarishmaB · Answer

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)

BrentGMATPrepNow · Answer

Let's rewrite the equation in   slope y-intercept form y =  m x +  b   , where  m is the slope of the line  and  b is the line's y-intercept

Take: 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 +  2 
So, the slope of the line is  k/3  and the y-intercept is  2

If the y-intercept is  2 , then the line  must  pass through the point (0,  2 )

Answer: B

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

With this prompt, we’re asked which of the following points will ALWAYS lie on the line (K)(X) + 3(Y) = 6 for EVERY possible value of K. This is a great ‘concept question’, meaning that you don’t have to do a lot of math to answer it if you recognize the concept involved (and that concept is a Number Property Rule that you probably already know…).

To start, if the value of K can vary – and the sum will always be 6 - then the relative values of X and/or Y will almost always change based on the value of K. From the way the question is worded though, we know that one of the co-ordinates will ALWAYS appear on the line. Thus, we have to look for an answer that ‘counters’ the fact that K could vary. If you don’t immediately see it, then you can TEST THE ANSWERS to prove it…

Answer A: (1,1)… With that co-ordinate, the equation would become…
K(1) + (3)(1) = 6…. So K can ONLY equal 3. This does NOT match what we were told.
Eliminate Answer A

Answer B: (0,2)… With that co-ordinate, the equation would become…
K(0) + (3)(2) = 6…. Since (3)(2) = 6, then and K(0) will ALWAYS equal 0, we have a correct equation and the value of K is IRRELEVANT (meaning that if K changes, the point will still appear on the line.

Final Answer:  B

GMAT Assassins aren’t born, they’re made,
Rich

CrackverbalGMAT · Answer

Solution:

To "must lie" for "every value of k", on the line the k term has to be removed.

This is possible if x = 0 as that would make k x =0 and the equation is k independent.

(option b) of (0,2) when plugged in suffices the condition.  (option b)

Devmitra Sen
GMAT SME

ScottTargetTestPrep · Answer

Solution:
 
Let’s express this equation in slope-intercept form by isolating y:

3y = -kx + 6

y = -k/3 x + 2

We see that this line has a y-intercept of 2, regardless of what the slope -k/3 is (hence regardless of the value of k as well). Since the ordered pair (0, 2) is in fact the y-intercept, we see, then, that the point (0, 2) must lie on the line.

Answer: B

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=2f5Us1oIQQY

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=HJT2IDrhEJM

ArnauG · Answer

To determine which point must lie on the line kx + 3y = 6 for every possible value of k, we can substitute each point into the equation and check if the equation holds true.

Let's substitute the points into the equation:

A. (1,1): k(1) + 3(1) = k + 3 ≠ 6 (not true for every possible value of k)
B. (0,2): k(0) + 3(2) = 0 + 6 = 6 (true for every possible value of k)
C. (2,0): k(2) + 3(0) = 2k + 0 = 2k ≠ 6 (not true for every possible value of k)
D. (3,6): k(3) + 3(6) = 3k + 18 ≠ 6 (not true for every possible value of k)
E. (6,3): k(6) + 3(3) = 6k + 9 ≠ 6 (not true for every possible value of k)

From the above calculations, we can see that only point (0,2) satisfies the equation kx + 3y = 6 for every possible value of k.

Therefore, the correct answer is (B) (0,2).

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

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GMAT Problem Solving (PS) Questions

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

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