The image shows a graph of the inequality $y > 2x - 1$. Here's an analysis of the inequality and the graph:

1. Equation: The boundary line is based on the equation $y = 2x - 1$, which is a linear equation. The slope $m = 2$ and the y-intercept is $-1$, meaning the line crosses the y-axis at $(0, -1)$.

2. Dashed Line: The graph shows a dashed blue line, which indicates that the boundary is not included in the solution set of the inequality, meaning points on the line do not satisfy the inequality.

3. Shaded Region: The inequality is $y > 2x - 1$, which means the region above the line should be shaded. The graph suggests shading the area above the dashed line.

Key Points:

• The dashed line represents the boundary line $y = 2x - 1$.
• Since the inequality is $y > 2x - 1$, the solution includes the area above the line (not including the line itself).

Would you like further clarification or any specific details on graphing inequalities?

Here are five related questions you could explore:

1. How do you graph the inequality $y \geq 2x - 1$, and what would change?
2. What is the difference between $y < 2x - 1$ and $y \leq 2x - 1$?
3. How do you find the points of intersection between two inequalities?
4. How does the slope of the line $y = 2x - 1$ influence the solution region?
5. How can you test a point to see if it satisfies an inequality?

Tip: To check which region to shade, substitute a test point (like $(0,0)$) into the inequality. If it satisfies the inequality, shade that region.