1. **State the problem:** We need to analyze the inequality $y > x + 4$. 2. **Understand the inequality:** This inequality represents all points $(x,y)$ in the coordinate plane where the $y$-value is strictly greater than the value of $x + 4$. 3. **Graphical interpretation:** The line $y = x + 4$ is the boundary. Points above this line satisfy $y > x + 4$. 4. **Formula and rules:** The boundary line is given by the equation: $$y = x + 4$$ Since the inequality is strict ($>$), the line itself is not included in the solution set. 5. **Summary:** The solution is the half-plane above the line $y = x + 4$. This inequality cannot be simplified further but can be graphed to visualize the solution region.