1. **State the problem:** We need to graph the linear equation $$-\frac{1}{2}x + y = \frac{3}{4}$$ in two variables $x$ and $y$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the $y$-intercept. Starting with the given equation: $$-\frac{1}{2}x + y = \frac{3}{4}$$ Add $\frac{1}{2}x$ to both sides: $$y = \frac{1}{2}x + \frac{3}{4}$$ 3. **Identify slope and intercept:** - Slope $m = \frac{1}{2}$ - $y$-intercept $b = \frac{3}{4}$ 4. **Find the $x$-intercept:** Set $y=0$ and solve for $x$: $$0 = \frac{1}{2}x + \frac{3}{4}$$ Subtract $\frac{3}{4}$: $$-\frac{3}{4} = \frac{1}{2}x$$ Multiply both sides by 2: $$2 \times -\frac{3}{4} = \cancel{2} \times \frac{1}{\cancel{2}} x$$ $$-\frac{6}{4} = x$$ Simplify: $$x = -\frac{3}{2}$$ 5. **Summary:** - $y$-intercept at $(0, \frac{3}{4})$ - $x$-intercept at $(-\frac{3}{2}, 0)$ - Slope $\frac{1}{2}$ means the line rises 1 unit for every 2 units it moves right. 6. **Final equation for graphing:** $$y = \frac{1}{2}x + \frac{3}{4}$$ This is the equation to plot the line with the intercepts and slope described above.