1. **Problem statement:** Find the equation of line L perpendicular to the line $2y + x = 1$ and passing through point $(2, -1)$. 2. **Rewrite the given line in slope-intercept form:** $$2y + x = 1 \implies 2y = 1 - x \implies y = \frac{1}{2} - \frac{x}{2} = -\frac{1}{2}x + \frac{1}{2}$$ The slope of this line is $m_1 = -\frac{1}{2}$. 3. **Find the slope of line L:** Lines perpendicular satisfy $m_1 \times m_2 = -1$. So, $$m_2 = -\frac{1}{m_1} = -\frac{1}{-\frac{1}{2}} = 2$$ 4. **Use point-slope form to find equation of line L:** Passing through $(2, -1)$ with slope $2$: $$y - (-1) = 2(x - 2) \implies y + 1 = 2x - 4 \implies y = 2x - 5$$ **Final answer:** $$\boxed{y = 2x - 5}$$