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.

Answer: D
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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.

MAGOOSH OFFICIAL SOLUTION:

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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.

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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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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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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