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# In the xy-coordinate system, line k has slope 1/2 and passes through

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Math Expert
Joined: 02 Sep 2009
Posts: 47948
In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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27 Mar 2015, 05:24
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25% (medium)

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73% (01:01) correct 27% (01:01) wrong based on 231 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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27 Mar 2015, 05:49
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.
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Re: In the xy-coordinate system, line k has slope 1/2 and passes through  [#permalink]

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30 Mar 2015, 03:49
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 2899 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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31 Oct 2016, 16:35
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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14 Mar 2018, 05:54
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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14 Mar 2018, 06:15
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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14 Mar 2018, 15:59
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 &nbs [#permalink] 14 Mar 2018, 15:59
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