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# In the xy-plane, if line l has negative slope and passes through the

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Math Expert
Joined: 02 Sep 2009
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In the xy-plane, if line l has negative slope and passes through the  [#permalink]

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25 May 2018, 01:13
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Difficulty:

55% (hard)

Question Stats:

62% (01:53) correct 38% (01:54) wrong based on 87 sessions

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In the xy-plane, if line l has negative slope and passes through the point (-4, q), is the x-intercept of line l positive?

(1) q < 0
(2) The slope of line l is 4

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

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26 May 2018, 01:01
1
According to statement 1, if q is less than 0, the point lies in the 3rd quadrant. Thus, it has to cut the negative x axis. Thus, x intercept will be negative. Hence, sufficient.

According to statement 2, slope of the line is -4, as is known that it is negative from the question stem, then we will get the following equation.

y+4 = -4(x - q)
Thus, y =-4x + 4q - 4
Putting, y = 0,

x = q - 1.

Thus for values of q greater than 1, x is positive, otherwise 0 and negative. Since, value of q is not given, hence, this statement is insufficient.

Hence, imo A.

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

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26 May 2018, 11:39
Bunuel wrote:
In the xy-plane, if line l has negative slope and passes through the point (-4, q), is the x-intercept of line l positive?

(1) q < 0
(2) The slope of line l is 4

Ans: A

Sol:
State 1) As it is given that line has negative slope ( downward direction from second quard to IV th) and q < 0 this means this point is in Third Quard. and thus X intercept of line will always be neative. [Sufficient]

State 2) Slope of the line is = -4 and one point is given (-4,q) but this does not provide any info from which we can identify the x intercept. (Not suff)

ans: A
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Re: In the xy-plane, if line l has negative slope and passes through the  [#permalink]

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23 Jun 2018, 11:44
In the xy-plane, if line l has negative slope and passes through the point (-4, q), is the x-intercept of line l positive?

(1) q < 0
(2) The slope of line l is 4

negative slop goes through quadrant II and IV. We have to find if it also goes through I or III. If it goes through III then x intercept has a -ve sign and if it goes through II then x intercept had +ve sign.

1) Q<0 . which means line goes through quadrant III so x-intercept is -ve. SUFFICIENT
2) we have only one co-ordinate and slope. NOT sufficient
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Re: In the xy-plane, if line l has negative slope and passes through the  [#permalink]

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11 Jul 2019, 14:25
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Re: In the xy-plane, if line l has negative slope and passes through the   [#permalink] 11 Jul 2019, 14:25
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