Question: What is an equation of the line that passes through the points $(-2, 3)$ and $(-4, -2)$?
1. **State the problem:** Find the equation of the line passing through points $(-2, 3)$ and $(-4, -2)$.
2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Calculate the slope:**
$$m = \frac{-2 - 3}{-4 - (-2)} = \frac{-5}{-4 + 2} = \frac{-5}{-2} = \frac{\cancel{-5}}{\cancel{-2}} = \frac{5}{2}$$
4. **Use point-slope form:**
The equation of the line is:
$$y - y_1 = m(x - x_1)$$
Using point $(-2, 3)$:
$$y - 3 = \frac{5}{2}(x - (-2)) = \frac{5}{2}(x + 2)$$
5. **Simplify:**
$$y - 3 = \frac{5}{2}x + 5$$
Add $3$ to both sides:
$$y = \frac{5}{2}x + 5 + 3$$
$$y = \frac{5}{2}x + 8$$
6. **Final answer:**
The equation of the line is:
$$y = \frac{5}{2}x + 8$$