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: \(\frac{0 - 7}{0 - (-4)}=\frac{k - 0}{14 - 0}\)

Simplify: \(\frac{-7}{4}=\frac{k}{14}\)

Cross multiply to get: \(4k = (-7)(14)\)

Divide both sides of the equation by 4 to get: \(k = \frac{(-7)(14)}{4}= \frac{-98}{4}=-24.5\)

Answer: D

Cheers,
Brent