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# Line l is defined by the equation y – 5x = 4 and line w is d

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Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 122
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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24 Feb 2013, 03:56
4
22
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:53) correct 32% (02:13) wrong based on 688 sessions

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Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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24 Feb 2013, 05:35
10
11
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.
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##### General Discussion
Intern
Joined: 05 Aug 2012
Posts: 15
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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24 Feb 2013, 06:03
1
Line L equation : y = 5x + 4

I think the wording of your problem got messed up... i.e. there is some typo error...

So Assuming 10y + 2x = 20 is line K. The equation of line K : = 10y = -2x - 20. Dividing by 10 throughout we get
y = ( -1/5 ) x - 2

Slope of line L = m1 = 5
Slope of line K = m2 = -1/5

The standard rule says that if the product of two slope is -1 then the two lines are perpendicular

m1 * m2 = > 5 * - 1/5 = -1

Hence the answer is D i.e. 90

Hope this helps
Senior Manager
Joined: 07 Apr 2012
Posts: 358
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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28 Sep 2014, 06:48
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.

Hi Bunuel,
If we are given two lines (and know their slopes), can we calculate the degree that their intersection makes?
What's the formula for that?
Manager
Joined: 06 Mar 2014
Posts: 239
Location: India
GMAT Date: 04-30-2015
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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10 Nov 2014, 08:20
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.

Bunuel,
Sorry for my ignorance but is it a fact that two lines in any plane, if they don't intersect, they MUST be parallel?
Math Expert
Joined: 02 Sep 2009
Posts: 52906
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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10 Nov 2014, 08:29
earnit wrote:
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.

Bunuel,
Sorry for my ignorance but is it a fact that two lines in any plane, if they don't intersect, they MUST be parallel?

On the GMAT, all figures lie in a plane unless otherwise indicated. So, lines l, w and k are in the same plane. Next, if two lines that are in the same plane do not intersect, the two lines are parallel. Thus, line k does not intersect line l, means that lines k and l are parallel.

Hope it's clear.
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Manager
Joined: 06 Mar 2014
Posts: 239
Location: India
GMAT Date: 04-30-2015
Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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10 Nov 2014, 08:32
Bunuel: Hope it's Clear

Me: Crystal.

Thank you.
Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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14 Jun 2017, 20:40
1
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

It is important to understand and have a visual map of this question- what this questions basically means when it states that all lines lie in one plane simply means- well within the context of the GMAT as Bunuel already stated- that all lines exist on a two dimensional plane. So if you draw out a chart/ plane with 4 quadrants as usual on a piece of paper then there's no way to have two lines that do not intersect and are not parallel. In simpler terms, if two lines do not intersect then they MUST be parallel. Also, do not confuse line k with l or w- basically this question gives you two equations for two lines because these lines are perpendicular.

Line L
10y= -2x -20=
y = -2/10x - 20
y= -1/5x - 2

Line W
y= 4 +5x
y= 5x + 4 ( commutative property of addition)

Because line K does not intersect L it MUST be parallel to L and if line K is parallel to L then it is also perpendicular to W- and perpendicular simply means it forms a 90 degree angle. Perpendicular lines are also important for circle questions on the GMAT. Some of the concepts should hopefully carry over- so some of the common traps and shortcuts in coordinate geometry problems on the GMAT will help with PS and DS questions in regular geometry and vice versa.
Intern
Joined: 12 Jun 2017
Posts: 9
Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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15 Jun 2017, 09:20
ronr34 wrote:
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me

The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

For more on Coordinate Geometry check: http://gmatclub.com/forum/math-coordina ... 87652.html

PS questions on Coordinate Geometry: http://gmatclub.com/forum/search.php?se ... &tag_id=41
DS questions on Coordinate Geometry: http://gmatclub.com/forum/search.php?se ... &tag_id=62

Hope it helps.

Hi Bunuel,
If we are given two lines (and know their slopes), can we calculate the degree that their intersection makes?
What's the formula for that?

Yes. Use the formula

TanX = m1-m2/(1+m1m2)

where X is the angle between the lines and m1 and m2 are the slopes.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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07 Sep 2018, 00:29
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Re: Line l is defined by the equation y – 5x = 4 and line w is d   [#permalink] 07 Sep 2018, 00:29
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