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by GmatKiss » Sun Oct 30, 2011 1:52 pm
In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y – 7, then k =

9
3
7/3
1
1/3
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by GMATGuruNY » Sun Oct 30, 2011 2:04 pm
GmatKiss wrote:In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y – 7, then k =

9
3
7/3
1
1/3
The equation of the line rephrased as y = mx+b:
3y-7 = x
3y = x+7
y = (1/3)x + 7/3.

Slope = 1/3.
Since (a,b) and (a+3,b+k) are two points on the line, and slope = (change in y/change in x), we get:
(b+k-b)/(a+3-a) = 1/3.
k/3 = 1/3.
k=1.

The correct answer is D.
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by shankar.ashwin » Sun Oct 30, 2011 4:38 pm
An alternate method;

Eq of the line is x=3y-7. Substitute any(x,y) which satisfies this equation. Lets assume (2,3). Now (a,b)=(2,3)

We need to find k for (2+3, 3+k) or (5,3+k)

5=3(3+k) - 7
3+k=4
k=1 D
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by GmatKiss » Mon Oct 31, 2011 12:35 am
Thanks a lot Mitch :)
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by Gokhra » Mon Oct 31, 2011 1:59 am
Just to share my method of solving:

The equation is x = 3y - some constant

As soon as I see it, I think "every time you increase y by 1, x increases by 3." The question asks exactly that, "How much do you increase y by to increase x by 3?"

Basically, instead of trying to solve the equations for variables, just restating the question helped me get to the answer very quickly.

Hope this will be helpful to someone!
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by vaibhavgupta » Mon Oct 31, 2011 5:24 am
GmatKiss wrote:In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y – 7, then k =

9
3
7/3
1
1/3
D it is! :)
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