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

[BTGmoderatorDC]

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

[Brent@GMATPrepNow]

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