Graph Inequality 6A6299

1. **State the problem:** We need to sketch the graph of the inequality $$y \geq -2x + 4$$. 2. **Understand the inequality:** This inequality represents all points $$ (x,y) $$ where $$ y $$ is greater than or equal to the line $$ y = -2x + 4 $$. The line itself is included because of the \geq symbol, so it will be drawn as a solid line. 3. **Graph the boundary line:** The line $$ y = -2x + 4 $$ has a slope of $$ -2 $$ and a y-intercept of $$ 4 $$. - Plot the y-intercept at $$ (0,4) $$. - Use the slope to find another point: from $$ (0,4) $$, go down 2 units and right 1 unit to reach $$ (1,2) $$. - Alternatively, the problem mentions the point $$ (2,0) $$ which also lies on the line. 4. **Draw the line:** Connect these points with a solid line because the inequality includes equality (\geq). 5. **Shade the correct region:** Since the inequality is $$ y \geq -2x + 4 $$, shade the region above the line. 6. **Summary:** The graph is a solid line with negative slope passing through $$ (0,4) $$ and $$ (2,0) $$, with the shaded region above the line, matching the description given.