1. **State the problem:** We need to graph two lines given by the equations: Line A: $2x - y = 5$ Line B: $x + 2y = 10$ 2. **Rewrite each equation in slope-intercept form $y = mx + b$ to easily graph them.** For Line A: $$2x - y = 5$$ Subtract $2x$ from both sides: $$-y = -2x + 5$$ Multiply both sides by $-1$: $$\cancel{-1} \times -y = \cancel{-1} \times (-2x + 5)$$ $$y = 2x - 5$$ For Line B: $$x + 2y = 10$$ Subtract $x$ from both sides: $$2y = -x + 10$$ Divide both sides by $2$: $$\frac{2y}{\cancel{2}} = \frac{-x + 10}{\cancel{2}}$$ $$y = -\frac{1}{2}x + 5$$ 3. **Interpret the slope and intercepts:** - Line A has slope $2$ and y-intercept $-5$. - Line B has slope $-\frac{1}{2}$ and y-intercept $5$. 4. **Graphing:** - For Line A, start at $(0, -5)$ on the y-axis and rise 2 units for every 1 unit run to the right. - For Line B, start at $(0, 5)$ on the y-axis and fall 1 unit for every 2 units run to the right. This will produce two lines intersecting at some point. Final equations for graphing: Line A: $y = 2x - 5$ Line B: $y = -\frac{1}{2}x + 5$