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In the x-y plane, If line k does not pass through the origin, is the s

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MathRevolution
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In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   02 Feb 2017, 01:12
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In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?

1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive
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0akshay0
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Re: In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   02 Feb 2017, 02:01
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MathRevolution wrote:
In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?

1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive



St I
let y = mx + c be the equation of the line.
x intercept => 0 = mx +c => x = -(c/m)
y intercept => y = c

y intercept = 4 * x intercept
c = 4 * (-(c/m))
m = -4
Slope is negative --------- Sufficient

St II
If the product of the y-intercept and the x-intercept of the line K is positive, then either both x,y intercepts must be negative or both intercepts must be positive
and therefore the slope of the line will be negative ---------- Sufficient

Hence Option D is correct
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In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   Updated on: 02 Feb 2017, 02:28
MathRevolution wrote:
In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?

1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive



1.
Y intercept is 4 times the x ..
X intercept=(M,0)
Y-Intercept=(0,4M)

Slope = 0-4m/m-0= -m/4m=-4.Suff.

B.
Two cases we can assume ..
1.X intercept and Y intercept will be -ve---Slope will be negative.
2.both positive-again slope is negative
we can plot in graph to check.
So D..
MathRevolution -- is my understanding correct

Originally posted by sobby on 02 Feb 2017, 02:08.
Last edited by sobby on 02 Feb 2017, 02:28, edited 1 time in total.
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In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   02 Feb 2017, 02:20
sobby wrote:
MathRevolution wrote:
In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?

1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive



1.
Y intercept is 4 times the x ..
X intercept=(M,0)
Y-Intercept=(0,4M)

Slope = M-0/0-4M= -m/4m=-1/4.Suff.

B.
Two cases we can assume ..
1.X intercept and Y intercept will be -ve---Slope will be negative.
2.both positive-again slope is negative
we can plot in graph to check.
So D..
MathRevolution -- is my understanding correct


The way you calculated the slope in St 1 is incorrect.
It must be other way round i.e Slope = (0-4M) / (M-0) = -4 (since slope is defined as rise over run)
:)
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Re: In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   02 Feb 2017, 02:26
0akshay0 wrote:
sobby wrote:
MathRevolution wrote:
In the x-y plane, If line k does not pass through the origin, is the slope of the line K negative?

1) The y-intercept of the line K is 4 times the x-intercept of the line K
2) The product of the y-intercept and the x-intercept of the line K is positive



1.
Y intercept is 4 times the x ..
X intercept=(M,0)
Y-Intercept=(0,4M)

Slope = M-0/0-4M= -m/4m=-1/4.Suff.

B.
Two cases we can assume ..
1.X intercept and Y intercept will be -ve---Slope will be negative.
2.both positive-again slope is negative
we can plot in graph to check.
So D..
MathRevolution -- is my understanding correct


The way you calculated the slope in St 1 is incorrect.
It must be other way round i.e Slope = (0-4M) / (M-0) = -4 (since slope is defined as rise over run)
:)


Yes, missed in haste...did other way around... :P
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Re: In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   03 Feb 2017, 02:02
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==> In the original condition, there are 2 variables(there are 2 variables for a line -> slope and y-intercept). In order to match with the number of equations, you need 2 equations. For 1) 1 equation and for 2) 1 equation, which is likely to make C the answer. Through 1) & 2), 1)=2) is derived and it is yes for each condition.

Hence, it is sufficient and the answer is D.
Answer: D
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Re: In the x-y plane, If line k does not pass through the origin, is the s [#permalink] New post   08 Oct 2023, 07:26
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Re: In the x-y plane, If line k does not pass through the origin, is the s [#permalink]
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