In the xy-plane, if line k has negative slope and passes : GMAT Data Sufficiency (DS)
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In the xy-plane, if line k has negative slope and passes

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In the xy-plane, if line k has negative slope and passes [#permalink]

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In the xy-plane, if line k has negative slope and passes through the point (s;-2), is the x-intercept of line k positive?

(1) s = 0
(2) The y-intercept of line k is negative.
[Reveal] Spoiler: OA

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Re: In the xy-plane, if line k has negative slope and passes [#permalink]

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In the xy-plane, if line k has negative slope and passes through the point (s;-2), is the x-intercept of line k positive?

Look at the diagram below:
Attachment:
Intercept.png
Intercept.png [ 11.68 KiB | Viewed 2725 times ]

(1) s = 0. Directly gives the y-intercept of line k: (0, -2). Since the y-intercept of line k is negative and the slope of line k is negative too then the x-intercept of line k must also be negative. Sufficient.

(2) The y-intercept of line k is negative. The same here: since the y-intercept of line k is negative and the slope of line k is negative too then the x-intercept of line k must also be negative.

Answer: D.
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Re: In the xy-plane, if line k has negative slope and passes [#permalink]

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Re: In the xy-plane, if line k has negative slope and passes [#permalink]

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In the xy-plane, if line k has negative slope and passes [#permalink]

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New post 17 Jan 2017, 10:38
enigma123 wrote:
In the xy-plane, if line k has negative slope and passes through the point (s;-2), is the x-intercept of line k positive?

(1) s = 0
(2) The y-intercept of line k is negative.


The general equation of a line is y = mx+b. There are two things to consider here:

    If the line passes through \((s,-2)\), then \(-2 = ms+b.\)
    The x-intercept of a line is given by \(x = \frac{-b}{m}\).


Now, since m is negative, the question is asking is b > 0?

(1) s = 0. From the first consideration above, this tells us that b = -2. Sufficient.

(2) The y-intercept is negative (b < 0). Sufficient.

Therefore, either statement is sufficient.

Answer: D
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Re: In the xy-plane, if line k has negative slope and passes [#permalink]

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New post 17 Jan 2017, 15:01
took some extra seconds to think of the possible options...
1 - x intercept is 0! statement 1 is sufficient.
2 - there is no possible way for x intercept to be positive - sufficient.

D must be the answer
Re: In the xy-plane, if line k has negative slope and passes   [#permalink] 17 Jan 2017, 15:01
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