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In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa

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In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post Updated on: 04 Jul 2018, 21:02
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In the xy-coordinate plane, the slope of line l is 3/4. Does line l pass through the point (-2/3, 1/2)?


(1) Line l passes through the point (4, 4).

(2) Line l passes through the point (-4, -2).

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Originally posted by kabilank87 on 23 Apr 2013, 01:07.
Last edited by Bunuel on 04 Jul 2018, 21:02, edited 3 times in total.
Renamed the topic and edited the question.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 23 Apr 2013, 03:53
4
4
let the line be: y=mx+c

where m is the slope and c is the y intercept.

so y=(3/4)x+c

Statement 1:
if the line passes through 4,4 then 4=(3/4) 4 + c.. That implies c = 1. hence the equation of the line is y=(3/4)x+1. Now you can find whether line passes through -2/3,1/2

Similarly for statement 2.

You don't need to calculate all of this. You need to tell whether the statement is 'sufficient' to get an answer. in general, when the slope and a point is given you can find the equation of the line. Therefore, you can find whether any random point lies on that line or not.

Hence D.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 23 Apr 2013, 03:08
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kabilank87 wrote:
In the XY - coordinate plane the slope of a line L is 3/4. Does the line L pass through point (-2/3 , 1/2 )

1, Line L pass through point (4,4)
2. Line L pass through point (-4,-2)


NO need to calculate anything. If you know two points on a line, you can calculate the unique slope for that line. From both the Fact statements, we can arrive at a unique slope and answer the Question Stem.

D.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 23 Apr 2013, 03:38
vinaymimani wrote:
kabilank87 wrote:
In the XY - coordinate plane the slope of a line L is 3/4. Does the line L pass through point (-2/3 , 1/2 )

1, Line L pass through point (4,4)
2. Line L pass through point (-4,-2)


NO need to calculate anything. If you know two points on a line, you can calculate the unique slope for that line. From both the Fact statements, we can arrive at a unique slope and answer the Question Stem.

D.


Hi Vinay,

Will you please explain with formulas or steps ?

Thanks in advance.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 23 Apr 2013, 03:56
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Quote:

Hi Vinay,

Will you please explain with formulas or steps ?

Thanks in advance.


If two unique points (x,y) and (p,q) are given for a line,the slope of this line = (q-y)/(p-x) or (y-q)/(x-p).

From F.S 1, we know that line passes through (4,4). Assume that it does pass through (-2/3,1/2). Then, the slope of the line has to be 3/4. Now the slope = (4-1/2)/[4-(-2/3)] = (7/2)/(14/3) = 3/4. Thus, it indeed passes through (-2/3,1/2). Sufficient.

From F.S 2, similarly, the slope = (-2-1/2)/[-4-(-2/3)] = (-5/2)/(-10/3) = 3/4. Thus, it passes through the given point. Sufficient.
Note that in case the slope didn't turn out to be 3/4, we would STILL be able to answer the question stem, with a YES or a NO.

D.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 24 Apr 2013, 18:17
Equation of the line can be formed by using the slope and a point using the slope-point form of the line equation. Both A and B provides for the point needed to get the equation. Using equation of line we can check for the required condition. D wins.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 01 Aug 2013, 02:19
1
kabilank87 wrote:
In xy-coordinate plane, the slope of line L is 3/4. Does line L pass through point (-2/3, 1/2)?

(1) Line L passes through (-4 ,4)
(2) Line L passes through (-4, -2)


Please note statement 1 has been changed from (4,4 ) to (-4, 4)

Well (-4,4) means line L does not pass through point (-2/3, 1/2)
so both the statements will contradict each other.

if statement 1 can be edited to the original format ( 4,4) that could help.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 01 Aug 2013, 02:28
stne wrote:
kabilank87 wrote:
In xy-coordinate plane, the slope of line L is 3/4. Does line L pass through point (-2/3, 1/2)?

(1) Line L passes through (-4 ,4)
(2) Line L passes through (-4, -2)


Please note statement 1 has been changed from (4,4 ) to (-4, 4)

Well (-4,4) means line L does not pass through point (-2/3, 1/2)
so both the statements will contradict each other.

if statement 1 can be edited to the original format ( 4,4) that could help.
Thanks


Thanks for noticing.
+1.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 30 Oct 2015, 21:45
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In xy-coordinate plane, the slope of line L is 3/4. Does line L pass through point (-2/3, 1/2)?

(1) Line L passes through (4 ,4)
(2) Line L passes through (-4, -2)

as the per the problem statement -
y = mx + c
y = ( 3/4 )x + c

now plug in the point (-2/3, 1/2)
we get
1/2 = ( -2/3) ( 3/4) x + c
on solving the above we get
c = 0

hence the question becomes c = 0 ?

St 1 ==> Line L passes through (4 ,4)
the slope of line L is 3/4

now use the equation y = mx + c
plus the values ...m = 3/4 and x = 4 , y = 4

on the solving the above we get c =1
no ..definite ans . Sufficient .

St 2 ==> solve similarly as statement 1
we again get c = 1

sufficient

hence D ans

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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 01 Nov 2015, 09:53
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In xy-coordinate plane, the slope of line L is 3/4. Does line L pass through point (-2/3, 1/2)?

(1) Line L passes through (4 ,4)
(2) Line L passes through (-4, -2)

In the original condition, we only need to know the slop and the y-intercept, but the slope is given to be 3/4, so we only have one variable. This means we require only 1 equation when there are 2 equations given from the 2 conditions; there is high chance (D) will be our answer.
From condition 1, the answer can be either yes or no, so it is sufficient,
and in condition 2, the answer also can be both yes and no, so it is sufficient as well, making the answer D.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 11 Jan 2016, 15:28
I did understand the explanation, but with difficulty.

Does someone knows where I can find good theory of line equations and slope formula and some excercises to practice with?

Thanks in advance :)
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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New post 31 Jan 2017, 18:42
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Slope equation between two points is slope = y2-y1/x2-x1

We know that our line has a slope of 3/4. Each of the statements also gives us a point on the line. All we really need to do is find whether the slope bwtween the point given and (-2/3,1/2) is dequal to 3/4 or not.

stat. (1) 4-1/2 / 4-(-2/3) = 3.5 / 4+2/3 = 7/2 / 14/3 = 7/2 * 3/14 = 1/2 * 3/2 = 3/4. the answer is yes. Sufficient

Stat. (2) -2-1/2 / -4-(-2/3) = -2.5 / -4+2/3 = -5/2 / -10/3 = -5/2 * 3/-10 = 1/2 * 3/2 = 3/4. the answer is yes. Sufficient

the answer is D.
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Re: In the xy-coordinate plane, the slope of line l is 3/4. Does line l pa  [#permalink]

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