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Math Expert V
Joined: 02 Sep 2009
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In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (02:03) correct 37% (01:59) wrong based on 253 sessions

### HideShow timer Statistics 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.

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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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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.

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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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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 56371
Re: In the xy-plane, line l passes through the point (-7, k). What is the  [#permalink]

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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: 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 [ 4.06 KiB | Viewed 4671 times ]

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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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_________________ Re: In the xy-plane, line l passes through the point (-7, k). What is the   [#permalink] 21 Aug 2018, 14:23
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