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# Two lines, k and m, intersect in the coordinate plane at point (a,b).

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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
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PathFinder007

HI Karishma,

Could you please explain following statement

y intercept of m is positive and x intercept in negative i.e. slope of m is positive ?

how the slope is coming positive.

Thanks.

What does y intercept positive mean? It means the line intersects the y axis at a point above 0. Similarly, what does x intercept negative mean? It means the line meets the x axis at a point to the left of 0. So try to draw such a line. It will always have positive slope.
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
@Sudish
Could you please check the the attachment. I have different graph, with same answer, i. e. a and b can either be positive or negative.
Attachments

XY.docx [11.63 KiB]

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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
+1 D.
The two ways in which the lines can be constructed have already been discussed above. It is clear that the point of intersection will lie in either the first or the third quadrant. In either case, a and b will have the same sign and hence, ab will always be positive. Both statements are sufficient to give us that information.
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
Re-phrase: (a,b) for lines k amd m will be only positive if that point lies in I or III quadrant. That is k and m must have positive slopes, that is negative intercepts for x-inercept for n=m and y intercept for k respectively.

1. Gives one of the above condition, suff
2. Gives the other condition. suff

D.
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
VeritasPrepKarishma
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@Sudish
Could you please check the the attachment. I have different graph, with same answer, i. e. a and b can either be positive or negative.

Both the diagrams are correct. They are the two different cases that are possible. Let me explain.

The question is: "Is ab positive?"
ab will be positive when either both a and b are positive or both a and b are negative. Both a and b will be positive in the first quadrant and both a and b will be negative in the third quadrant. So if your lines intersect in the first or the third quadrant, ab will be positive.

Each statement alone tells you two things:
1. y intercept of m is positive and x intercept in negative i.e. slope of m is positive
2. y intercept of k is negative and x intercept is positive i.e. slope of k is positive

In this case, k and m cannot intersect in the second or fourth quadrant. They must intersect in the first of third quadrant as shown by the two diagrams you guys have put up.
Hence each statement alone is sufficient.

HI Karishma,

Could you please explain following statement

y intercept of m is positive and x intercept in negative i.e. slope of m is positive ?

how the slope is coming positive.

Thanks.
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
sudish

Thanks a lot! You have the best explanation for the 2nd statement by giving an illustration of the two lines in the X Y coordinate plane.

Thanks again!
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
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Re: Two lines, k and m, intersect in the coordinate plane at point (a,b). [#permalink]
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