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

[BTGModeratorVI]

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)

Answer: D
Source: Magoosh

[swerve]

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)

Answer: D
Source: Magoosh

Consider equation of line be \(y=mx+c\), where \(m\) is slope and \(c\) is \(y-\)intercept. From the data in the question, \(m=\dfrac{1}{2}\) and \(c=5\)

Hence, our equation becomes \(y=\dfrac{1}{2}x+5\)

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 \(2\).

[Brent@GMATPrepNow]

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)

Answer: D
Source: Magoosh

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

[Scott@TargetTestPrep]

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)

Answer: D

Solution:

The ordered pair (0,5) means that the y-intercept of line k is 5. Using the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept, we see that 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