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In the xy-coordinate plane, which of the following points

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by Brent@GMATPrepNow » Mon Aug 20, 2018 6:52 am
AAPL wrote:Official Guide

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

A. (1,1)
B. (0,2)
C. (2,0)
D. (3,6)
E. (6,3)
APPROACH #1:

The key here is "for every possible value of k"
So, let's assign a value of k and see what happens.
How about k = 0?
When k = 0, the equation becomes: (0)x + 3y = 6
Simplify: 3y = 6
Solve: y = 2

So, in this case, the y-coordinate must be 2!
Check the answer choices...only answer choice B works!

Answer: B

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Brent
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by Brent@GMATPrepNow » Mon Aug 20, 2018 6:56 am
AAPL wrote:Official Guide

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

A. (1,1)
B. (0,2)
C. (2,0)
D. (3,6)
E. (6,3)

OA B.
APPROACH #2:

Rewrite the equation in slope y-intercept form y = mx + b, where m is the slope of the line and b is the line's y-intercept

Take: kx + 3y = 6
Subtract kx from both sides: 3y = 6 - kx
Divide both sides by 3 to get: y = 2 - kx/3
Rewrite as: y = (k/3)x + 2
So, the slope of the line is k/3 and the y-intercept is 2

If the y-intercept is 2, then the line must pass through the point (0, 2)

Answer: B

Cheers,
Brent
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by Jeff@TargetTestPrep » Mon Aug 20, 2018 10:42 am
AAPL wrote:Official Guide

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

A. (1,1)
B. (0,2)
C. (2,0)
D. (3,6)
E. (6,3)
If a point is on a line with the equation kx + 3y = 6 for every possible value of of k, then x must be 0, since then kx = k(0) = 0. So then we have 3y = 6 or y = 2. Thus the point (0, 2) will always be on the line regardless what the value of k is.

Alternate Solution:

Let's rewrite the equation kx + 3y = 6 in slope-intercept form y = mx + b:
kx + 3y = 6

3y = -kx + 6

y = -kx/3 + 2

We see that the y-intercept of this line is at 2, and the ordered pair for this y-intercept is (0,2). In other words, when x = 0, then y = 2, and it doesn't matter what k equals because the term containing k is equal to 0.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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