1. The problem is to graph the linear inequality $y > 1$. 2. This inequality means we want all points where the $y$-coordinate is greater than 1. 3. First, graph the line $y = 1$. This is a horizontal line crossing the y-axis at 1. 4. Since the inequality is strict ($>$, not $\geq$), the line itself is not included. We represent this by drawing a dashed line. 5. The solution region is above the line $y = 1$, which includes all points with $y$ values greater than 1. 6. To verify, pick a test point. For example, $(0, 2)$: substituting gives $2 > 1$, which is true, so this region is shaded. 7. The graph therefore shows a dashed horizontal line at $y=1$ with shading above it.