1. **State the problem:** We are given a line passing through points $(-1, -2)$ and $(1, -4)$ and need to find its slope $m$ and y-intercept $b$. 2. **Formula for slope:** The slope $m$ of a line passing 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:** Using the points $(-1, -2)$ and $(1, -4)$: $$m = \frac{-4 - (-2)}{1 - (-1)} = \frac{-4 + 2}{1 + 1} = \frac{-2}{2} = -1$$ 4. **Formula for y-intercept:** The line equation is $y = mx + b$. To find $b$, substitute one point and the slope into the equation: $$y = mx + b \implies b = y - mx$$ 5. **Calculate the y-intercept:** Using point $(-1, -2)$ and $m = -1$: $$b = -2 - (-1)(-1) = -2 - 1 = -3$$ 6. **Final equation of the line:** $$y = -1x - 3$$ **Answer:** The slope is $m = -1$ and the y-intercept is $b = -3$.