To determine which graph represents the inequality $2x > y$, let's first rewrite it in slope-intercept form for easier visualization.

The given inequality is: $2x > y$

Rewriting it in slope-intercept form ($y = mx + b$): $y < 2x$

This tells us that the line $y = 2x$ is the boundary of the inequality. The inequality symbol $<$ means that we are considering the area below the line.

Key Characteristics of the Graph

1. Line Equation: The boundary line is $y = 2x$. This line has a slope of 2 and passes through the origin (0, 0).
2. Dashed Line: The boundary line should be dashed because the inequality is strict ($<$), meaning points on the line itself are not included in the solution.
3. Shading: The region below the dashed line $y = 2x$ should be shaded, indicating the solution set.

Conclusion

The correct graph would feature:

• A dashed line representing $y = 2x$.
• The shaded region below this line.

Would you like more details on how to plot the graph or have any questions?

Here are some related questions:

1. How do you graph inequalities with more than one condition (e.g., $y > 2x$ and $y < x + 3$)?
2. What changes if the inequality symbol is $\geq$ or $\leq$?
3. How do you determine if a point is a solution to an inequality graphically?
4. What are the steps to convert inequalities into slope-intercept form?
5. How do inequalities affect the shape of linear regions on a coordinate plane?

Tip: When dealing with inequalities, always pay attention to whether the boundary line is dashed or solid; this indicates if the line itself is included in the solution.