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

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Magoosh

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

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

OA D

[Brent@GMATPrepNow]

Magoosh

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

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

OA D

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


Cheers,
Brent