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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.

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. _________________

Kabilan.K Kudos is a boost to participate actively and contribute more to the forum

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.

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.

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

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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.

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

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11 Oct 2014, 18:19

Hello from the GMAT Club BumpBot!

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

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24 Oct 2015, 12:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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01 Nov 2015, 09:53

Expert's post

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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