Find the x-intercept of the line passing through the points A(-1, -2) and B(1, -1).

1. Problem Description

Find the x-intercept of the line passing through the points A(-1, -2) and B(1, -1).

2. Solution Steps

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

The formula for the slope is:

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

Substituting the coordinates of A and B, we have:

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

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

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

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

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

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

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

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

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

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

Subtract $\frac{1}{2}$ from both sides:

$2 - \frac{1}{2} = \frac{1}{2}x$

$\frac{4}{2} - \frac{1}{2} = \frac{1}{2}x$

$\frac{3}{2} = \frac{1}{2}x$

Multiply both sides by 2:

$3 = x$

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

3. Final Answer

(3, 0)

C