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

Did you know that the inequality \( y \leq -2x + 1 \) describes a region on the coordinate plane? The line itself, represented by \( y = -2x + 1 \), has a slope of -2, meaning it goes down steeply as x increases. The area below this line (including the line itself) represents all the solutions to the inequality. Visualizing this can help understand the behavior of linear inequalities! When graphing inequalities like this, a common mistake is forgetting to shade the correct side of the line. Always remember that for \( \leq \) or \( \geq \) signs, you include the boundary line with a solid line, indicating that points on the line satisfy the inequality. For \( < \) or \( > \), you use a dashed line, as those points are not included. Happy graphing!