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02 Sep 2010, 12:52
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A
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Difficulty:
45%
(medium)
Question Stats:
65% (01:52) correct
35%
(02:03)
wrong
based on 2363
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If line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation \(y = (1-m)x + b +1\).
(2) k intersects the line with equation \(y = 2x + 3\) at the point (2, 7).
(1) k is parallel to the line with equation \(y = (1-m)x + b +1\).
(2) k intersects the line with equation \(y = 2x + 3\) at the point (2, 7).
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02 Sep 2010, 13:19
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If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?
\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).
So we are asked to find the value of \(m\).
(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.
(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.
Answer: A.
\(y=mx+b\) is called point-intercept form of equation of a line. Where: \(m\) is the slope of the line; \(b\) is the y-intercept of the line; \(x\) is the independent variable of the function \(y\).
So we are asked to find the value of \(m\).
(1) k is parallel to the line with equation y = (1-m)x + b +1 --> parallel lines have the same slope --> slope of this line is \(1-m\), so \(1-m=m\) --> \(m=\frac{1}{2}\). Sufficient.
(2) k intersects the line with equation y = 2x + 3 at the point (2, 7) --> so line k contains the point (2,7) --> \(7=2m+b\) --> can not solve for \(m\). Not sufficient.
Answer: A.
26 Mar 2012, 14:15
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For Coordinate Geometry check:
For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
Hope it helps.
24. Coordinate Geometry
- Theory
- Questions
Math: Coordinate Geometry
Beauty of Coordinate geometry
Dealing with Tangents on the GMAT
DS Questions
PS Questions
For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
Hope it helps.
