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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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15 May 2012, 21:26
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66% (02:16) correct 34% (01:10) wrong based on 215 sessions

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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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16 May 2012, 01:09
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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 [ 11.68 KiB | Viewed 2906 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.

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

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28 Nov 2013, 14:18
Hello from the GMAT Club BumpBot!

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

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22 Jan 2015, 14:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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17 Jan 2017, 11:38
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.

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

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17 Jan 2017, 16:01
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.

Re: In the xy-plane, if line k has negative slope and passes   [#permalink] 17 Jan 2017, 16:01
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