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# Lines n and p lie in the xy-plane. Is the slope of line n

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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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23 Oct 2016, 22:38
rohit8865 wrote:
Bunuel wrote:
nglekel wrote:
Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

If line p has a negative y-intercept then its slope is positive and it will still be more than the slope of n, with positive y-intercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive y-intercept and you'll easily see the answer.

Hope it helps.

Experts

for below attached fig ...getting 2 diff.. answers.....

Responding to a pm:

I am not sure I understand why you say you are getting two different answers. In both diagrams, the slope of n is less than the slope of p. We are comparing actual values of the slopes, not just the absolute values.
So say slope of n is -2 in both cases. Slope of p in the first diagram will be -1/2 and slope of p in the second diagram would be about 1.
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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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13 Nov 2016, 06:02
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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30 Nov 2016, 13:11
Here is a great resource to understand slope. You can plug in values and see how things change:
https://www.desmos.com/calculator/nuokqfhfxi

Hope this helps
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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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22 Apr 2017, 13:23
Bunuel wrote:
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

Algebraic approach:

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

We have two lines: $$y_n=m_1x+b_1$$ and $$y_p=m_2x+b_2$$. Q: $$m_1<m_2$$ true?

(1) Lines n and p intersect at the point (5,1) --> $$1=5m_1+b_1=5m_2+b_2$$ --> $$5(m_1-m_2)=b_2-b_1$$. Not sufficient.

(2) The y-intercept of line $$n$$ is greater than the y-intercept of line $$p$$ --> y-intercept is value of $$y$$ for $$x=0$$, so it's the value of $$b$$ --> $$b_1>b_2$$ or $$b_2-b_1<0$$. Not sufficient.

(1)+(2) $$5(m_1-m_2)=b_2-b_1$$, as from (2) $$b_2-b_1<0$$ (RHS), then LHS (left hand side) also is less than zero $$5(m_1-m_2)<0$$ --> $$m_1-m_2<0$$ --> $$m_1<m_2$$. Sufficient.

For more on this topic check Coordinate Geometry Chapter of Math Book: http://gmatclub.com/forum/math-coordina ... 87652.html

Hope it helps.

Hi Bunuel,

Can you share some similar questions to practice on this topic? Also, what would be the level of such a question? <650?
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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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23 Apr 2017, 02:28
ashikaverma13 wrote:
Bunuel wrote:
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

Algebraic approach:

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

We have two lines: $$y_n=m_1x+b_1$$ and $$y_p=m_2x+b_2$$. Q: $$m_1<m_2$$ true?

(1) Lines n and p intersect at the point (5,1) --> $$1=5m_1+b_1=5m_2+b_2$$ --> $$5(m_1-m_2)=b_2-b_1$$. Not sufficient.

(2) The y-intercept of line $$n$$ is greater than the y-intercept of line $$p$$ --> y-intercept is value of $$y$$ for $$x=0$$, so it's the value of $$b$$ --> $$b_1>b_2$$ or $$b_2-b_1<0$$. Not sufficient.

(1)+(2) $$5(m_1-m_2)=b_2-b_1$$, as from (2) $$b_2-b_1<0$$ (RHS), then LHS (left hand side) also is less than zero $$5(m_1-m_2)<0$$ --> $$m_1-m_2<0$$ --> $$m_1<m_2$$. Sufficient.

For more on this topic check Coordinate Geometry Chapter of Math Book: http://gmatclub.com/forum/math-coordina ... 87652.html

Hope it helps.

Hi Bunuel,

Can you share some similar questions to practice on this topic? Also, what would be the level of such a question? <650?

The difficulty level of a question is given in the tags. It's 600-700 level question.

All DS Coordinate Geometry Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=41
All PS Coordinate Geometry Problems to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=62

Hope it helps.
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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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07 Dec 2017, 09:50
BANON wrote:
Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5 , 1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

We need to determine whether the slope of line n is less than the slope of line p.

Statement One Alone:

Lines n and p intersect at the point (5,1).

If the two lines intersect at a point, they are not parallel and hence their slopes are not equal (unless they are identical lines). So the slope of one line must be greater than the slope of the other line. However, we can’t determine which line has the greater slope. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

The y-intercept of line n is greater than the y-intercept of line p.

Knowing that the y-intercept of one line is greater than the y-intercept of the other does not allow us to determine which line has the greater slope.

For example, line n could have a y-intercept 2 and slope 3, and line p could have a y-intercept 1 and slope 2. In this case, line p has the lesser slope. However, it’s also possible that line n could have a y-intercept 2 and slope 2, and line p could have a y-intercept 1 and slope 3. In which case, line n has the lesser slope. Statement two alone is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

Knowing the point where the two lines intersect and the relationship of the y-intercept of each line allows us to determine which line has the lesser slope.

Even though we don’t know the actual y-intercept of each line, we know that the y-intercept of line n is greater than that of line p. So we can let the y-intercept of line n be b, and that of line p be c where b > c.

Thus, line n passes through (0, b), and line p passes through (0, c). Both lines also pass through (5, 1). Let’s calculate their slopes:

Slope of line n = (1 – b)/(5 – 0) = (1 – b)/5

Slope of line p = (1 – c)/(5 – 0) = (1 – c)/5

Now let’s determine whether (1 – b)/5 < (1 – c)/5.

Is (1 – b)/5 < (1 – c)/5 ?

Is 1 – b < 1 – c ?

Is –b < –c ?

Is b > c ?

Since, from the information in statement two, we know that b is greater than c, we have answered the question: the slope of line n is indeed less than that of line p.

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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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13 Dec 2017, 20:35
Am I right in my understanding that since the question asks for whether the slope of line n is greater than the slope of p, we need to consider only actual values and not absolute values.

If the question had asked for whether line n is steeper than line p, then we would have had to consider absolute values and in this second case, the answer will actually have been E?

Bunuel or Karishma or other experts please clarify.

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Re: Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]

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13 Dec 2017, 20:38
dramamur wrote:
Am I right in my understanding that since the question asks for whether the slope of line n is greater than the slope of p, we need to consider only actual values and not absolute values.

If the question had asked for whether line n is steeper than line p, then we would have had to consider absolute values and in this second case, the answer will actually have been E?

Bunuel or Karishma or other experts please clarify.

Yes, the question asks whether $$m_1<m_2$$ is true (not whether $$|m_1|<|m_2|$$ is true). Every solution on the previous two pages answers exactly this question.
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Re: Lines n and p lie in the xy-plane. Is the slope of line n   [#permalink] 13 Dec 2017, 20:38

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