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If Line k in the xy-plane has equation y = mx + b, where m

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If Line k in the xy-plane has equation y = mx + b, where m [#permalink] New post 02 Sep 2010, 11:52
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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).
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Re: Line slope [#permalink] New post 02 Sep 2010, 12:19
Expert's post
udaymathapati wrote:
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).


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 --> cannot solve for m. Not sufficient.

Answer: A.

For more on this issues please check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Re: If Line k in the xy-plane has equation y = mx + b, where m [#permalink] New post 16 Aug 2014, 05:05
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Re: If Line k in the xy-plane has equation y = mx + b, where m   [#permalink] 16 Aug 2014, 05:05
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