Given three points $A(3, 8)$, $B(4, m)$, and $C(-1, 4)$, we are told that they lie on the same straight line. We need to find the value of $m$.

1. Problem Description

Given three points $A(3, 8)$, $B(4, m)$, and $C(-1, 4)$, we are told that they lie on the same straight line. We need to find the value of $m$.

2. Solution Steps

If three points lie on the same line, then the slope between any two pairs of points must be the same.

Let's find the slope between points A and C:

$slope_{AC} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 8}{-1 - 3} = \frac{-4}{-4} = 1$

Now, let's find the slope between points A and B:

$slope_{AB} = \frac{m - 8}{4 - 3} = \frac{m - 8}{1} = m - 8$

Since A, B, and C are collinear (lie on the same line), the slopes $slope_{AC}$ and $slope_{AB}$ must be equal. Therefore,

$m - 8 = 1$

Solving for $m$:

$m = 1 + 8 = 9$

3. Final Answer

The value of $m$ is

9. The correct answer is C.