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Math Expert V
Joined: 02 Sep 2009
Posts: 53768
In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 77% (01:35) correct 23% (01:37) wrong based on 279 sessions

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In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?

A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)

Kudos for a correct solution.

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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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1
Consider equation of line be y= mx +c, where m is slope and c is y intercept. From the data in the question, m = 1/2 and c = 5.

So our equation becomes, $$y = (1/2)x + 5$$

Now, just substitute values of x-coordinate and see if the y-coordinate fits in. Option D stands out, for x = -2, y = 4 and not 2.
Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Bunuel wrote:
In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?

A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: possiblepointsonline_text.PNG [ 21.16 KiB | Viewed 3916 times ]

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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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1
From the prompt, we can derive the equation of line K:

5=1/2(0)+5 --> y =(1/2)x+5

The only point that, when plugged into this equation is true, is option D and therefore the correct answer.
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In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Bunuel pushpitkc niks18 Hatakekakashi
amanvermagmat chetan2u

I agree with OE, but it is far too time consuming to check each and every
answer choice. Any efficient way to do this?
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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Bunuel pushpitkc niks18 Hatakekakashi
amanvermagmat chetan2u

I agree with OE, but it is far too time consuming to check each and every
answer choice. Any efficient way to do this?

Hi,

You will have to generally substitute as Question asks which of the following, you can ofcourse make it easier..
1) 1/2 means change of 1 in y gives increase of 2 in x..
So (0,5)..
A) (-10,0)
Decrease of (5-0) should give 2*-5=-10.., so (-10,0) is ok
B) (8,9)
Increase of (9-5=4) should give 2*4=8.., so (8,9) is ok
C)(3,6.5)
Increase of (6.5-5=1.5) should give 2*1.5=3.., so (3,6.5) is ok
D) (-2,2)
Decrease of (5-2=3) should give 2*-3=-6.., so (-2,2) is Not o..
ok it should be (-6,2)
E (-8,1)
Decrease of (5-1=4) should give 2*-4=-8.., so (-8,1) is ok
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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Bunuel wrote:
In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?

A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)

The equation for line k is y = (1/2)x + 5. Let’s see which set of points cannot lie on line k.

A. (-10, 0)

0 = (1/2)(-10) + 5

0 = 0

(-10, 0) lies on line K.

B. (8, 9)

9 = (1/2)(8) + 5

9 = 9

(8, 9) lies on line k.

C. (3, 6.5)

6.5 = (1/2)(3) + 5

6.5 = 6.5

(3, 6.5) lies on line k.

D. (-2, 2)

2 = (1/2)(-2) + 5

2 ≠ 4

(-2, 2) is not on line k.

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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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Top Contributor
Bunuel wrote:
In the xy-coordinate system, line k has slope 1/2 and passes through point (0, 5). Which of the following points cannot lie on line k?

A. (-10, 0)
B. (8, 9)
C. (3, 6.5)
D. (-2, 2)
E. (-8, 1)

Kudos for a correct solution.

Let's first determine the equation of line k

A quick approach is the write the equation of line k in slope y-intercept form: y = mx + b, where m = slope and b = y-intercept.
We're told that the slope = 0.5 and the point (0,5) tells us that the y-intercept is 5
So, the equation of line k is: y = 0.5x + 5

Now that we know the equation of line k, a point will be ON the line if the coordinates (x, y) satisfy the equation.
So, let's take each answer choice and plug the x- and y-coordinates into the equation.

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.
For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... -questions

E. (-8, 1)
Plug x = -8 and y = 1 into the equation (y = 0.5x + 5) to get: 1 = (0.5)(-8) + 5
This works!!!
So, (-8, 1) is ON the line.
ELIMINATE E

D. (-2, 2)
Plug x = -2 and y = 2 into the equation (y = 0.5x + 5) to get: 2 = (0.5)(-2) + 5
Doesn't work. So, (-2, 2) is NOT on the line.

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Test confidently with gmatprepnow.com  Re: In the xy-coordinate system, line k has slope 1/2 and passes through   [#permalink] 05 Sep 2018, 06:39
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# In the xy-coordinate system, line k has slope 1/2 and passes through

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