If the points X(2, -1), Y(3, k), Z(1, 4) are colinear, then the value of k is

The points are $X(2, -1)$, $Y(3, k)$, $Z(1, 4)$.

For collinear points, they all lie on the same straight line. This means the slope between any two pairs of points must be equal.

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For $X(2, -1)$ and $Y(3, k)$:

Slope of $XY = \dfrac{k - (-1)}{3 - 2}$

$= \dfrac{k + 1}{1}$

$= k + 1$

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For $X(2, -1)$ and $Z(1, 4)$:

Slope of $XZ = \dfrac{4 - (-1)}{1 - 2}$

$= \dfrac{4 + 1}{-1}$

$= \dfrac{5}{-1}$

$= -5$

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Since the points are collinear:

$k + 1 = -5$

$k = -5 - 1$

$k = -6$

Therefore, $k = -6$.