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Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a

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Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]  02 Aug 2017, 08:28
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Question Stats:

51% (02:05) correct 48% (02:23) wrong based on 33 sessions

Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a y-intercept of 6, and the point (6, 4) lies on line P.

 Quantity A Quantity B The measure of the largest angle created by the intersection of line M and line N The measure of the largest angle created by the intersection of line M and line P

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 344 [0], given: 66

Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]  21 Sep 2017, 09:18
Any help here?
Intern
Joined: 23 Sep 2017
Posts: 18
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Kudos [?]: 7 [0], given: 6

Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]  21 Oct 2017, 03:40

Here is my solution

slope of m=3
slope of n=5/2
slope of P=0
tanx= (m1-m2)/(1-m1m2)

calculating this way, first tangent value is 1/17 and second is 3..
as the angle increase, tangent value increase, hence second is a bigger number.
Moderator
Joined: 18 Apr 2015
Posts: 5860
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Kudos [?]: 1147 [3] , given: 5456

Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]  23 Oct 2017, 11:36
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Quote:
The measure of the angles created at the intersection of any two lines is a function of the relative slopes of the lines. Since you are given enough information to solve for the slope of each of the lines involved, you can eliminate choice (D) immediately—you have enough information for a solution.
The slopes of lines M and N can be calculated directly since you are provided with equations that describe the lines. In the generic equation y = mx + b, m is the slope of the line and b is the y-intercept. Thus, theslope of M is 3 and the slope of N is $$\frac{5}{2}$$ (you obtain the slope of line N by dividing both sides of the equation for N by 2). Since you know that line P contains the points (0, 6) and (6, 4), you can compute the slope of the line as follows:

Slope = $$\frac{\triangle y}{\triangle x} = \frac{(6 - 4)}{(0 - 6)} = -\frac{1}{3}$$ The slope of line Pis the negative reciprocal of the slope of line M; by definition this means that the lines are perpendicular. It follows that every angle created by the intersection of lines M and P must be 90°.

Since lines M and N are not perpendicular or parallel, you know that the inter­section creates two angles of less than 90° and two angles of greater than 90°.

Thus, Quantity A is greater.

Hope this helps.

regards
_________________
Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a   [#permalink] 23 Oct 2017, 11:36
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