The inequality given is $y > 4$. This means we are looking for a graph where:

1. There is a horizontal dashed line at $y = 4$ (indicating that the boundary line is not included in the solution).
2. The shading is above this line, representing values of $y$ that are greater than 4.

Looking at the three options provided in the image:

• The first graph shows a dashed line at $y = 4$ with shading above it, which matches the inequality $y > 4$.
• The second graph has shading below a different line, so it does not match.
• The third graph has shading across the entire plane, which also does not match.

Therefore, the correct choice is the first graph.

Would you like further details on why this selection matches the inequality?

Here are some related questions to consider:

1. How would the graph look for the inequality $y \geq 4$?
2. How would a graph of $y < -3$ differ visually?
3. What would change if the inequality was $x > 4$ instead of $y > 4$?
4. How does shading direction help in determining the inequality's solution?
5. Why is a dashed line used instead of a solid line for $y > 4$?

Tip: When graphing inequalities, remember that a dashed line is used for strict inequalities (>, <), while a solid line is used for inclusive inequalities (≥, ≤).