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22 May 2010, 14:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:36) correct
33%
(01:38)
wrong
based on 284
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In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?
(1) s = 0
(2) The y-intercept of line k is negative
(1) s = 0
(2) The y-intercept of line k is negative
22 May 2010, 15:57
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Drawing method:
(1) Line k passes through the point (0, -2) and has negative slope. Line k can be something like this:
Attachment:
1.png [ 9.16 KiB | Viewed 8131 times ]
(2) The y-intercept of line k is negative and line has negative slope. Line k can be something like this:
Attachment:
2.png [ 9.87 KiB | Viewed 8157 times ]
Answer: D.
Algebraic approach:
Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)); \(x\) is the independent variable of the function \(y\).
X-intercept is the value of \(x\) for \(y=0\) --> \(x_{intercept}=-\frac{b}{m}\).
Question: is \(-\frac{b}{m}>0\). As given that slope is negative (\(m<0\)), basically the question becomes is \(b>0\)?
(1) Line k passes through the point (0, -2) --> \(-2=0*m+b\) --> \(b=-2<0\). Answer to the question is NO. Sufficient.
(2) The y-intercept of line k is negative --> as y-intercept is value of \(b\), so we are directly told that \(b<0\). Answer to the question is NO. Sufficient.
Answer: D.
For more on this issue refer to the Coordinate Geometry chapter of the Math book (link in my signature).
Hope it helps.
General Discussion
22 May 2010, 15:11
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Can someone help me on how to approach and solve such problems. Thanks in advance.
In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?
(1) s = 0
(2) The y-intercept of line k is negative
y=mx+c
given that m is -ve & the line passes through (s,-2)
the equation of the line will be
y= -mx+c ( substitute (s,-2) in the equation )
therefore,
y+2 =-m(x-s)
y+2=-mx+ms
question is x intercept of line is +ve.,
to find x intercept, put y=0. so the equation will be,x=(ms-2)/m;
Condition 1) if S=0; then x will be -ve
Condition 2) The y-intercept of line k is negative
we cant deducew any thing from it.
Ans - A)
In the xy-plane, if line k has negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?
(1) s = 0
(2) The y-intercept of line k is negative
y=mx+c
given that m is -ve & the line passes through (s,-2)
the equation of the line will be
y= -mx+c ( substitute (s,-2) in the equation )
therefore,
y+2 =-m(x-s)
y+2=-mx+ms
question is x intercept of line is +ve.,
to find x intercept, put y=0. so the equation will be,x=(ms-2)/m;
Condition 1) if S=0; then x will be -ve
Condition 2) The y-intercept of line k is negative
we cant deducew any thing from it.
Ans - A)
