To find the y-intercept of the line passing through the points $(-2, -2)$ and $(2, -4)$, we can follow these steps:

Step 1: Find the slope (m)

The slope formula is:

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

Using the points $(-2, -2)$ and $(2, -4)$:

$m = \frac{-4 - (-2)}{2 - (-2)} = \frac{-4 + 2}{2 + 2} = \frac{-2}{4} = -\frac{1}{2}$

Step 2: Use the point-slope form of a line equation

The point-slope form is:

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

Let's use the point $(-2, -2)$:

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

Simplifying:

$y + 2 = -\frac{1}{2}(x + 2)$ $y + 2 = -\frac{1}{2}x - 1$ $y = -\frac{1}{2}x - 1 - 2$ $y = -\frac{1}{2}x - 3$

Step 3: Find the y-intercept

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation $y = -\frac{1}{2}x - 3$:

$y = -\frac{1}{2}(0) - 3 = -3$

Thus, the y-intercept is $(0, -3)$.

Answer:

The correct choice is A. (0, -3).

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How do you calculate the slope between two points on a line?
2. What is the point-slope form of a line and how is it useful?
3. How does the y-intercept relate to the equation of a line?
4. How would the slope change if the two points were reversed?
5. Can the y-intercept ever be the same as one of the given points?

Tip: The y-intercept is always found by setting $x = 0$ in the equation of a line.