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Difficulty:
25%
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Question Stats:
75% (01:34) correct
25%
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wrong
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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.
_________________
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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Bunuel
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: https://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.
Answer: D
General Discussion
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.
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.
Bunuel
MAGOOSH OFFICIAL SOLUTION:
Attachment:
possiblepointsonline_text.PNG [ 21.16 KiB | Viewed 13494 times ]
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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.
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.
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?
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?
adkikani
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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ScottTargetTestPrep
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Joined: 14 Oct 2015
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Expert reply
Posts: 22,738
Bunuel
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.
Answer: D
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