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Posts: 191
14 Mar 2012, 01:04
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C
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Difficulty:
95%
(hard)
Question Stats:
44% (02:11) correct
56%
(02:10)
wrong
based on 435
sessions
History
Date
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In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?
(1) The x-intercept of line k is less than the y-intercept of line k.
(2) The slope of line k is less than -2.
(1) The x-intercept of line k is less than the y-intercept of line k.
(2) The slope of line k is less than -2.
15 Mar 2012, 09:15
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In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?
Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\).
(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of \(x\) for \(y=0\), so it's \(-\frac{b}{m}\). The statement says that: \(-\frac{b}{m}<b\) --> multiply by negative \(m\) and flip the sign of the inequality: \(-b>bm\) --> \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? --> is \(m<-1\). We don't know that. Not sufficient.
(2) The slope of line k is less than -2. Insufficient on its own.
(1)+(2) From (1) the question became: "is \(m<-1\)?" and (2) says that \(m<-2\). Sufficient.
Answer: C.
Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line and \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)). So, basically we are asked whether \(b>0\).
(1) The x-intercept of line k is less than the y-intercept of line k --> x-intercept is value of \(x\) for \(y=0\), so it's \(-\frac{b}{m}\). The statement says that: \(-\frac{b}{m}<b\) --> multiply by negative \(m\) and flip the sign of the inequality: \(-b>bm\) --> \(b(m+1)<0\). Now, in order \(b>0\) to be true \(m+1\) should be negative, so the question becomes: is \(m+1<0\)? --> is \(m<-1\). We don't know that. Not sufficient.
(2) The slope of line k is less than -2. Insufficient on its own.
(1)+(2) From (1) the question became: "is \(m<-1\)?" and (2) says that \(m<-2\). Sufficient.
Answer: C.
14 Mar 2012, 01:51
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vdadwal
let me try:
we have line k say: y=mx+c
we need to find if c>0
1) x-intercept, i.e. y=0
x=-c/m
y-intercept, i.e. x=0
y=c
hence -c/m<c
=> c*((1/m)+1)>0
i.e. for different value of "m", "c" can be both positive and negative
hence insufficient
2) cant infer anything about c
insufficient
1+2
if m<-2
c*(m+1)<0 (m<0 hence sign change)
as m<-2
hence m+1<-1
i.e. negative
i.e. c>0
Sufficient
hence C
hope it helps..!!!
