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C
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Difficulty:
55%
(hard)
Question Stats:
64% (02:00) correct
36%
(01:57)
wrong
based on 349
sessions
History
Date
Time
Result
Not Attempted Yet
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
(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
19 Jan 2015, 14:02
Kudos
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Bunuel
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
19 Jan 2015, 23:16
Kudos
Bookmarks
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
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
