1. \( y \leq-2 x+1 \)

The given inequality is \( y \leq -2x + 1 \). To analyze this inequality, we can follow these steps: 1. **Identify the boundary line**: The boundary line of the inequality is given by the equation \( y = -2x + 1 \). This is a linear equation. 2. **Determine the slope and y-intercept**: - The slope \( m \) is -2, which means for every unit increase in \( x \), \( y \) decreases by 2 units. - The y-intercept \( b \) is 1, which means the line crosses the y-axis at the point (0, 1). 3. **Graph the boundary line**: - Plot the y-intercept (0, 1). - Use the slope to find another point. From (0, 1), move down 2 units and right 1 unit to reach the point (1, -1). - Draw a dashed line through these points because the inequality is \( \leq \), indicating that points on the line are not included in the solution set. 4. **Shade the appropriate region**: - Since the inequality is \( y \leq -2x + 1 \), we shade the region below the line, which represents all the points where \( y \) is less than or equal to the value of \( -2x + 1 \). This gives us the solution set for the inequality \( y \leq -2x + 1 \). If you need further analysis or specific points within this region, please let me know!