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In the xy-plane, line l passes through the point (-7, k). What is the

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In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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New post 19 Jan 2015, 06:02
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In the xy-plane, line l passes through the point (-7, k). What is the value of the y-intercept of line l ?

(1) The x-intercept of line l is 4.

(2) Line l and line n are parallel and the equation of line n is y=x+5

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Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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New post 19 Jan 2015, 14:02
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Bunuel wrote:
In the xy-plane, line l passes through the point (-7, k). What is the value of the y-intercept of line l ?

(1) The x-intercept of line l is 4.

(2) Line l and line n are parallel and the equation of line n is y=x+5

Kudos for a correct solution.


Answer : C

My approach:

let the equation of the line be y =mx+c, where m is the slope and c is the constant.
from stem, line passes through (-7,k). This is a point on the line.
k=-7m+c ------> (1)

from 1: x intercept is 4, so (4,0) is a point on the line

4m + c = 0 ---> (2)

solving 1 and 2 for m and c in terms of k we have: m = k/11 and c = -4k/11
equation of the line is then y = kx/11-4k/11
y intercept is when x = 0 => y intercept = -4k/11, as k can be any value --> not sufficient

from 2: line is parallel to y = x+5, so slope of the line is 1. equation of the line reduces to
y = x+c. (c = k+7, from stem as m = 1).
y -intercept = c = k+7 : NSF

from 1+2 combined
(4,0) is a point on the line from 2, y= x+k+7 => k = -11. From this y - intercept = -4*-11/11= 4. sufficient
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Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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New post 19 Jan 2015, 23:16
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1
Here we go----

To find out the y intercept of a line... put x = 0 in the equation of the line

Let the equation of the line-------------> y = mx + c
line l passes through the point (-7, k)---------------------> k = -7m + c ---(1)


St1: The x-intercept of line l is 4.
So the line passes through (4,0)
0 = 4m + c ----> 4m + c = 0 ----(2)
Clearly not sufficient

St2: Line l and line n are parallel and the equation of line n is y=x+5
Slopes of line l and line n are equal
From (1)
y = x + c

Clearly not sufficient

Combining St1 and St2
m = 1
Put in (2)

c = -4


Hence option C is correct
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Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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New post 04 Apr 2016, 11:05
please tell me where i am wrong ?

line passes thru (4,0) and (-7,k)
we can calculate m = k-0/-7-4
m= -k/11

now using the slope we can write the equation as -

y=mx+ c
or y = -k/11x + c


points on line should satisfy equation : -
so putting y as k and x as -7 cant we get the value of C???

Please explain on this where am i going wrong
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Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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New post 04 Apr 2016, 12:03
rohitkumar77 wrote:
In the xy-plane, line l passes through the point (-7, k). What is the value of the y-intercept of line l ?

(1) The x-intercept of line l is 4.

(2) Line l and line n are parallel and the equation of line n is y=x+5

please tell me where i am wrong ?

line passes thru (4,0) and (-7,k)
we can calculate m = k-0/-7-4
m= -k/11

now using the slope we can write the equation as -

y=mx+ c
or y = -k/11x + c


points on line should satisfy equation : -
so putting y as k and x as -7 cant we get the value of C???

Please explain on this where am i going wrong


For (1) we have the following:

Image

The point (-7, k) can be anywhere on red line, giving different lines passing through (-7, k) and (4, 0), which will give different y-intercept of line l.

Hope it's clear.
Attachment:
1.png
1.png [ 4.06 KiB | Viewed 3729 times ]

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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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