The problem states that a line $l$ passes through the points $(2, -1)$ and $(-1, m)$. The slope of the line is given as $2$. We need to find the value of $m$.

1. Problem Description

The problem states that a line $l$ passes through the points $(2, -1)$ and $(-1, m)$. The slope of the line is given as $2$. We need to find the value of $m$.

2. Solution Steps

The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$

In this problem, we are given the points $(2, -1)$ and $(-1, m)$, and the slope is $2$. So, we have:

$$2 = \frac{m - (-1)}{-1 - 2}$$

$$2 = \frac{m + 1}{-3}$$

Multiply both sides by $-3$:

$$-6 = m + 1$$

Subtract 1 from both sides:

$$m = -6 - 1$$

$$m = -7$$

3. Final Answer

The value of $m$ is $-7$.