1. The problem asks to write the slope-intercept form equation of the line passing through the point $(-2, -1)$ with slope $\frac{1}{2}$. 2. Recall the slope-intercept form of a line is given by: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. We know $m = \frac{1}{2}$ and the line passes through $(-2, -1)$, so substitute these values into the equation to find $b$: $$-1 = \frac{1}{2} \times (-2) + b$$ 4. Simplify the multiplication: $$-1 = \frac{1}{2} \times -2 + b = -1 + b$$ 5. Solve for $b$ by adding 1 to both sides: $$-1 + 1 = -1 + b + 1$$ $$0 = b$$ 6. So, the y-intercept $b = 0$. 7. Substitute $m$ and $b$ back into the slope-intercept form: $$y = \frac{1}{2}x + 0$$ 8. Simplify the equation: $$y = \frac{1}{2}x$$ Final answer: The slope-intercept form of the line is $$y = \frac{1}{2}x$$