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If the line passes through the origin, what is the value of k?

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by BTGmoderatorDC » Wed Feb 19, 2020 6:09 pm
GMAT_PS_Magoosh_85.png
If the line passes through the origin, what is the value of k?


A. -8
B. -12.5
C. -18
D. -24.5
E. -28



OA D

Source: Magoosh
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Re: If the line passes through the origin, what is the value of k?

by Brent@GMATPrepNow » Thu Feb 20, 2020 6:52 am
BTGmoderatorDC wrote: ↑
Wed Feb 19, 2020 6:09 pm
 GMAT_PS_Magoosh_85.png

If the line passes through the origin, what is the value of k?


A. -8
B. -12.5
C. -18
D. -24.5
E. -28



OA D

Source: Magoosh
Since the line passes through the origin, we know that the point (0, 0) also lies on the line.

Key property: The slope between any two points on a line will always be the same
This means: the slope between points (-4, 7) and (0, 0) must be equal to slope between points (0, 0) and (14, k)

We can now apply the slope formula to write: (0 - 7)/[0 - (-4)] = (k - 0)/(14 - 0)
Simplify: -7/4 = k/14
Cross multiply to get: 4k = (-7)(14)
Divide both sides of the equation by 4 to get: k = (-7)(14)/4 = -98/4 = -24.5

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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