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

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Question Stats: 39% (01:59) correct 61% (01:50) wrong based on 87 sessions

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In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2
(2) r > 0

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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: In the xy-plane, if line m has negative slope and passes through the  [#permalink]

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Bunuel wrote:
In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2
(2) r > 0

Similar questions to practice:
https://gmatclub.com/forum/in-the-xy-pl ... 32647.html
https://gmatclub.com/forum/in-the-xy-pl ... 35197.html
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In the xy-plane, if line m has negative slope and passes through the  [#permalink]

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Bunuel wrote:
In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2
(2) r > 0

Let the equation of the line be y = mx + c, where m is slope. Here, X & Y-Intercept is X = -c/m, Y = c. The question = Is -c/m positive.
1) As the line passes through (r,6) implies, c = 6.. As m is negative X intercept will be positive... So, Sufficient.
2) As r > 0, 6 = rm + c. Now, X = -c/m or -(6-rm)/c --> rm-6/m --> r - (6/m)... As m is -ve and r>0, X intercept will be positive.

Hence, D.
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GMAT 1: 680 Q48 V35 In the xy-plane, if line m has negative slope and passes through the  [#permalink]

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Bunuel wrote:
In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2
(2) r > 0

The line is $$y=m·x+b$$.

To know whether the x-intercept is positive or negative is enough to find out whether the y-intercept (b) is positive (YES) or negative (NO).

We know that:

m is negative.
$$(r,6)$$ fulfills the equation of the line so: $$6=m·r+b | b=6-m·r$$ Since m is negative, the answer will be a resounding YES if r is positive or WE CANNOT KNOW if r is negative sine everything would depends upon whether m·r is greater or less than 6.

S1.

$$b=6+\frac{1}{2}·r$$

We don´t the sign of r.

INSUFF.

S2.

$$b=6-m·r$$

If m is negative (from question) and r is positive (predicted info needed), b is positive and thus the x-intercept is positive.

SUFF.

AC: B

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

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rahul16singh28 wrote:
Bunuel wrote:
In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2
(2) r > 0

Let the equation of the line be y = mx + c, where m is slope. Here, X & Y-Intercept is X = -c/m, Y = c. The question = Is -c/m positive.
1) As the line passes through (r,6) implies, c = 6.. As m is negative X intercept will be positive... So, Sufficient.
2) As r > 0, 6 = rm + c. Now, X = -c/m or -(6-rm)/c --> rm-6/m --> r - (6/m)... As m is -ve and r>0, X intercept will be positive.

Hence, D.

Hi Rahul

The fact that line passes through (r, 6) doesn't necessarily imply that c (or y intercept) is 6 (your first statement analysis). Eg, if r = 6, then we only have the data that this line passes through the point (6,6). Now this line could also pass through the origin, in which case the y intercept of this line will be 0. OR this line passing through the point (6,6) could also pass through a point (0, -2) in which case y intercept of this line will be negative.

If we were given that r=0, then we should have concluded that the line is passing through (0,6) and thus its y intercept is 6. Re: In the xy-plane, if line m has negative slope and passes through the   [#permalink] 23 Jan 2018, 08:36
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