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If k and ℓ are lines in the xy-plane, is the slope of k less than the

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If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

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New post 02 Aug 2018, 23:58
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A
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C
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E

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Question Stats:

67% (01:09) correct 33% (01:11) wrong based on 201 sessions

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If k and ℓ are lines in the xy-plane, is the slope of k less than the slope of ℓ ?


(1) The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.
(2) Lines k and ℓ intersect on the positive y-axis.


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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

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New post 03 Aug 2018, 02:27
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1
To find if the slope of k less than the slope of ℓ

Statement 1

The x-intercept of line k is positive, and the x-intercept of line ℓ is negative.

Case 1

K can have a +ve slope when k rises upward while running from left to right and ℓ can have a -ve slope when ℓ slides downward while running from left to right

=> slope of line k > slope of line ℓ

Case 2

K can have a -ve slope when k slides downwards while running from left to right and ℓ can have a +ve slope when ℓ rises upward while running from left to right

=> slope of line k < slope of line ℓ

Statement 1 is not sufficient

Statement 2

Lines k and ℓ intersect on the positive y-axis. Both the above mentioned cases are still possible

Statement 2 is not sufficient

Combining statements 1 and 2

Since x-intercept of line k is positive and y-intercept of line k is positive => K has negative slope

Since x-intercept of line ℓ is negative and y-intercept of line ℓ is positive => ℓ has positive slope

=> slope of line ℓ > slope of line k

Statements 1 and 2 together are sufficient

Hence option C
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

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New post 05 Aug 2018, 12:23
Equation: y=mx+c

Case 1 for line k: x intercept is -c/m>0
Case 1 for line l: x intercept is -c/m<0

Statement 1 is not Sufficient as in both the cases, either c could be -ve or m could be -ve

Case 2: Y intercept is positive => c is positive in the equation for both lines

Statement 2 is not Sufficient as in both the cases, slope information is not there

Combining

Case 1 for line k: x intercept is -c/m>0 , given c >0 , m is -ve
Case 1 for line l: x intercept is -c/m<0, given c>0, m is +ve

=> slope l>slope k or slope k<slope l - Sufficient

C

Hope this helps! :-)
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the  [#permalink]

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New post 06 Sep 2018, 08:12
I cannot emphasize more: 99.99% of xy-plane questions (DS/PS) can be solved by drawing. Don't mess with formulas here.
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Re: If k and ℓ are lines in the xy-plane, is the slope of k less than the &nbs [#permalink] 06 Sep 2018, 08:12
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