1. The problem asks to draw and label three lines on a grid and then shade the region satisfying three inequalities. 2. The lines are: (i) $y=1$ which is a horizontal line crossing the y-axis at 1. (ii) $x=2$ which is a vertical line crossing the x-axis at 2. (iii) $x+y=7$ which can be rewritten as $y=7-x$; this line crosses the x-axis at 7 and the y-axis at 7. 3. For the inequalities: - $y \geq 1$ means the region above or on the line $y=1$. - $x \geq 2$ means the region to the right of or on the line $x=2$. - $x + y \leq 7$ means the region below or on the line $x+y=7$. 4. The region $R$ is the intersection of these three regions, i.e., the area on or above $y=1$, on or to the right of $x=2$, and on or below $x+y=7$. 5. To summarize: - Draw the horizontal line $y=1$. - Draw the vertical line $x=2$. - Draw the diagonal line $x+y=7$. - Shade the region where all three inequalities hold true. This completes the solution for the first question.