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In the xy plane, line x goes through the point (a,1) and lin

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BabySmurf
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In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   Updated on: 04 Jan 2023, 05:31
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In the xy plane, line x goes through the point (a,1) and line y goes through the point (1,b). If the lines x and y intersect, is the slope of x bigger than the slope of y?

(1) a > b
(2) |a| > |b|

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Appreciate if someone could help with the following question. Appreciate also referrals/links to similar questions to digest the subject/theory behind this better. Thanks.
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E

Originally posted by BabySmurf on 22 Nov 2013, 01:34.
Last edited by Bunuel on 04 Jan 2023, 05:31, edited 2 times in total.
Renamed the topic and edited the question.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   22 Nov 2013, 02:16
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BabySmurf wrote:
In the xy plane, line x goes through the point (a,1) and line y goes through the point (1,b). If the lines x and y intersect, is the slope of x bigger than the slope of y?

(1) a > b
(2) |a| > |b|

Appreciate if someone could help with the following question. Appreciate also referrals/links to similar questions to digest the subject/theory behind this better. Thanks.


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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   22 Aug 2018, 19:37
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Hope the solution below helps

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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   22 Nov 2013, 02:08
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BabySmurf wrote:

In the xy plane, line x goes through the point (a,1) and line y goes through the point (1,b). If the lines x and y intersect, is the slope of x bigger than the slope of y?
(1) a > b
(2) |a| > |b|


From F.S 1, Assume a=1,b=0.

From the graph,line y is represented as blue and has a slope of 0.Thus, For the green line,which passes through (1,1), the slope is negative and thus less than the slope of line y

For the red line, which passes through (1,1), the slope is positive and more than the slope of line y.Insufficient.

From F.S 2, assuming the same set as a=1,b=0, we have the same result as above.

Taking both together , we have nothing new to add.

E.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   17 Dec 2019, 06:13
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If the lines x and y intersect, is the slope of x bigger than the slope of y?

Any two lines in the plane will always intersect unless they are parallel( have equal slope), it does not matter which has bigger slope .



So, it is not possible to answer, which has bigger slope

Answer E

BabySmurf wrote:
In the xy plane, line x goes through the point (a,1) and line y goes through the point (1,b). If the lines x and y intersect, is the slope of x bigger than the slope of y?

(1) a > b
(2) |a| > |b|

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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   24 Nov 2013, 04:13
hard one, is it e.

I just draw and feel.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   24 Aug 2018, 00:24
great explanation above
we should use algebra not drawing for this type, because doing so is quicker.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   06 Sep 2018, 08:05
thangvietnam wrote:
great explanation above
we should use algebra not drawing for this type, because doing so is quicker.


How long will it take for you to make all this algebra? Drawing and answering took 3 min, and I got the right answer.
Althought the question can be approached logicaly: to know the slope of any line we have to know at least 2 points.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   28 Apr 2021, 15:00
Best bet here is to draw it?

In the xy plane, line x goes through the point (a,1) and line y goes through the point (1,b). If the lines x and y intersect, is the slope of x bigger than the slope of y?

(1) a > b

Suppose (a,1) = (4,1) and (1,b) = (1,-1)

We can draw a horizontal line running through (4,1) and any line with a slope running through (1,-1). Flip the lines.

Insufficient.

(2) |a| > |b|

Same use case as above.

Insufficient.

Answer is E.
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   13 Nov 2022, 11:49
For this question, I think we need to understand the basic idea when we draw a line in coordinate geometry.

for every slope, we need to identify two points that create a line. One could be the intersecting point such as (a,1) and (1,b) but what about the other point??? is its origin (0,0) or any specific y intercept??
We don't know that.

Hence, answer E
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink] New post   04 Jan 2023, 05:24
It took me 30 secs. May be my logic and reasoning is stupid but like to share.
we need point of intersection to get the slopes of each line. Even we make equations for lines we have not enough information to get the point of intersection.So can not determine the slope using both the statements.
even by using formula,slope= -y intercept/x intercept , we are not able to determine the slope

above reasoning may sound stupid or not, I get the answer in 30sec
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Re: In the xy plane, line x goes through the point (a,1) and lin [#permalink]
04 Jan 2023, 05:24
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