If lines y=mx+b and x=y+bm intersect at a degrees angle

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If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

16 Nov 2012, 03:45

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If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree

[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Nov 2012, 05:26, edited 1 time in total.

Renamed the topic.

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Re: If lines y=mx+b [#permalink]

16 Nov 2012, 03:59

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Marcab wrote:

If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree

To find the angle between two lines, we need to know the slope of both lines. But as shown in the figure, this angle "a" can be either "x" or "y". But since we are given that a<90, we can find out which angle is required because x + y = 180. The slope of the second line is obviously 1. So the question is basically asking for the value of m.

1) Sufficient

2) We get y = bx + b. b is still unknown. Insufficient.

Answer is hence A.

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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

15 Feb 2013, 03:21

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m= tan x.
So x= tan inverse(m).
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

23 Nov 2012, 06:12

Marcab wrote:

If lines y=mx+b and x=y+bm intersect at a degrees angle (where a<90 ), what is the value of angle a ?

(1) m=2

(2) m=b

Source: Jamboree

We can find the angle of intersection b/w any 2 lines if we knw the values of their individual slopes.

For y = x + bm, slope is 1; for y = mx + b, slope is "m"
(1) Tan (a) = (m - 1)/(1 + 1*m); tan(a) < 90 if its value is +ve;since m-1>0, no need to add/subtract from 180.
Since statement 2 gives m=2, it is sufficient.
(2) Test y=x+1, y=2x+2 and y=3x+3 with "y=x - 1, y=x-4, and y=x-9"
y=x+1 and y=x gives 0 degrees
y=2x+2 and y=x-4 gives a diffrent value...INSUFF
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

15 Feb 2013, 02:51

Folks,
I understand A is sufficient to find the angle.. but how do you find the angle?
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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

15 Feb 2013, 03:58

Marcab wrote:

m= tan x.
So x= tan inverse(m).

but m is slope of which line out of the that intersect? :shock:

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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

20 Feb 2013, 16:07

m is the slope of the line
y=mx+b

If you draw an equation for this line, you will find m to be the slope of the line and b to be the intersect on y axis(when x=0). This is called the slope-intercept form of line equation and you memorizing it will help you deal with such questions. The form of such lines is
y=(slope)x+y-intersect

The other line x=y+bm can be written in a similar fashion

y=x-bm.

Going by the above stated formula, since the coefficient of x=1, slope =1. The y-intersect of the line is bm.

Hope that clarifies your doubt.

Sachin9 wrote:

Marcab wrote:

m= tan x.
So x= tan inverse(m).

but m is slope of which line out of the that intersect? :shock:

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Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink]

05 Mar 2013, 18:25

Angle between 2 lines is m1-m2/1+m1m2 ..

We already know slope of line X = Y + bm.

Option A tells slope of line A - so suffcient but option B tells nothing so not sufficient

Re: If lines y=mx+b and x=y+bm intersect at a degrees angle [#permalink] 05 Mar 2013, 18:25

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If lines y=mx+b and x=y+bm intersect at a degrees angle

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If lines y=mx+b and x=y+bm intersect at a degrees angle

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