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In the xy coordinate plane, which of the following

This topic has 2 expert replies and 1 member reply
canbtg Senior | Next Rank: 100 Posts Default Avatar
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In the xy coordinate plane, which of the following

Post Wed Jul 01, 2015 9:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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)

    OA

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    Post Wed Jul 01, 2015 10:03 am
    canbtg 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)

    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

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    Ian Stewart GMAT Instructor
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    Post Wed Jul 01, 2015 2:33 pm
    canbtg 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 ?
    I'd do exactly what Brent did, but maybe it's useful to see a bit more of the theory here. If we write the equation of any line in the form y = mx + b, then m is the slope of the line, and b is the y-intercept (where the line meets the y-axis). So if we rewrite the equation above in that form, we find:

    y = (-k/3)x + 2

    So we know exactly one point on the line - the y-intercept is 2, so (0, 2) is on the line for sure. But we know nothing about the slope without some info about k, and if we know nothing about the slope, the line could go anywhere as you move away from the y-axis. So we don't know any other points on the line besides the y-intercept.

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    nikhilgmat31 Legendary Member Default Avatar
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    Post Fri Jul 03, 2015 12:28 am
    we need not to find value of K.

    simply plugin in answer values.

    (0,2) is answer.

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