1. The problem asks to shade the area that is not true for the inequality $y > -x + 7$. 2. The boundary line is given by the equation $y = -x + 7$. 3. Since the inequality is strict ($>$), the boundary line is dashed, indicating points on the line are not included. 4. To find the area not true for $y > -x + 7$, we need to shade the region where $y \leq -x + 7$. 5. This means shading the area on or below the line $y = -x + 7$. 6. The line passes through points $(0,7)$ and $(7,0)$, so the shaded region includes all points satisfying $y \leq -x + 7$. Final answer: Shade the region on or below the dashed line $y = -x + 7$ to represent the area not true for $y > -x + 7$.