The problem asks us to find the x-intercept of the line passing through the points $A(-1, -2)$ and $B(1, -1)$. The x-intercept is the point where the line intersects the x-axis, which means the y-coordinate of that point is 0.

1. Problem Description

The problem asks us to find the x-intercept of the line passing through the points $A(-1, -2)$ and $B(1, -1)$. The x-intercept is the point where the line intersects the x-axis, which means the y-coordinate of that point is

0.

2. Solution Steps

First, we need to find the slope of the line passing through points $A(-1, -2)$ and $B(1, -1)$. The slope $m$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of points A and B, we get:

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

Now that we have the slope, we can use the point-slope form of a line:

$y - y_1 = m(x - x_1)$

Using point A $(-1, -2)$ and the slope $m = \frac{1}{2}$, we have:

$y - (-2) = \frac{1}{2}(x - (-1))$

$y + 2 = \frac{1}{2}(x + 1)$

To find the x-intercept, we set $y = 0$:

$0 + 2 = \frac{1}{2}(x + 1)$

$2 = \frac{1}{2}(x + 1)$

Multiply both sides by 2:

$4 = x + 1$

$x = 4 - 1$

$x = 3$

So, the x-intercept is the point $(3, 0)$.

3. Final Answer

The x-intercept of the line is $(3, 0)$. Therefore, the answer is C. $(3, 0)$.