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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
Any help here?
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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
2
I think answer B is correct.. please help..

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.
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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
Carcass wrote:
OE

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





Can you explain how did you conclude that the angles created by line M and line N will be greater than 90 and not less 90?
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Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
1
tanθ= (m2 – m1 ) / (1+m1m2)

A

m2=3,m1=2.5
thus tanθ= .5/8.5
=> θ=30 degree(approx)

B
m for P is 0
=> A>B => Answer (A)
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Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
3
Ans: A
because Line M and N are almost parallel but not parallel in true sense.
to find the intersection of M and N, write 'y' in both equations of M and N in terms of 'x' and then make them equal i.e.
3x+10=5/2x-16
solving above for x gives, x=-52, which means at x=-52 both lines intersect and from this it can also be concluded that the largest angle > 90 because both lines do not intersect at 90 degree.

for P, simply use the slope formula, m=(y2-y1)/(x2-x1)
(x1,y1)=(0,6) and (x2,y2)=(6,4)
therefore slope of P = -1/3 which is negative reciprocal of slope of line M, which has slope of 3.
so, the maximum angle of intersection between P and M is 90 and minimum is also 90.
therefore, Qty A > Qty. B.
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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
1
This is a good question that can be solved within 30 seconds if you know the trick.
We can solve for the slope of line P and get -1/3.
So, Line M and Line P are perpendicular. So, the maximum angle between lines M and P is also 90 degrees.
We also know that lines M[slope = 3] and P[slope = 5/2] are neither parallel nor perpendicular looking at the slopes.
And the maximum angle between such lines is always going to be > 90 degrees.
So, option A is the answer.
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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
I didn't think about perpendicular slopes. The way I solved it took longer but still less than 2 mins. We had enough info to draw roughly to scale, so I drew it out, and drawing you see A is clearly bigger than B.
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Re: Line M is y = 3x + 10. Line N is 2y = 5x- 6. Line P has a [#permalink]
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