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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]

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02 Sep 2010, 12:52
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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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02 Sep 2010, 13:19
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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.

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]

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16 Aug 2014, 06:05
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Re: If Line k in the xy-plane has equation y = mx + b, where m [#permalink]

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30 Jun 2016, 00:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If Line k in the xy-plane has equation y = mx + b, where m   [#permalink] 30 Jun 2016, 00:42
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