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

Question

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 .

santorasantu · Answer

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

DesiGmat · Answer

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

rohitkumar77 · Answer

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

Bunuel · Answer

For (1) we have the following: https://gmatclub.com/forum/download/file.php?id=29809 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. 1.png

exc4libur · Answer

y=mx+b; y-intercept when x=0, y=0+b, y=b, what is b=?
(-7,k): y=mx+b, k=-7m+b, b=k+7m

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

x-intercept when y=0: 0=4m+b, b=-4m

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

parallel lines have the same slope: m_n=m_l=1

(1&2)   sufic

b=-4m=-4(1)=-4

Ans (C)

TestPrepUnlimited · Answer

Analyzing the question:

We are not really given any information so we would still like two pieces of information to confirm a line.

Statement 1: 
This is one piece of information, we need another piece. Insufficient.

Statement 2: 
The slope is 1. This is just one piece of information, we need another piece. Insufficient.

Combined: 
Now we have two pieces that are both meaningful, we can confirm a line. Sufficient.

Ans: C

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