Graph Inequality 3Db474
1. State the problem: Graph the inequality $3x+23x+2$.
3. Identify the boundary line: the equation of the boundary is $$y=3x+2$$.
4. Line style: draw the boundary as a dashed line because the inequality is strict ($<$ or $>$ excludes the boundary).
5. Find intercepts to help sketch: the y-intercept is at $(0,2)$ and the x-intercept is at $(-\frac{2}{3},0)$.
6. Determine which side to shade: pick a test point like $(0,0)$ and substitute into $y>3x+2$ to check; since $0>2$ is false, do not shade below the line, so shade the region above the line.
7. Final answer: the graph is the half-plane above the dashed line $y=3x+2$, not including the line itself.