Grach the inequality. yleqslant -2x+1

To graph the inequality \( y \leq -2x + 1 \), follow these steps:<br /><br />1. **Graph the boundary line**: First, graph the equation \( y = -2x + 1 \). This is a straight line with a slope of -2 and a y-intercept of 1.<br /><br /> - To plot this line, start at the y-intercept (0, 1).<br /> - Use the slope to find another point. Since the slope is -2, it means for every 1 unit you move to the right on the x-axis, you move 2 units down on the y-axis. So, from (0, 1), move to (1, -1).<br /><br />2. **Draw the line**: Connect these points with a straight line. Since the inequality is \( \leq \) (less than or equal to), the line should be solid, indicating that points on the line are included in the solution.<br /><br />3. **Shade the region**: Since the inequality is \( y \leq -2x + 1 \), shade the region below the line. This represents all the points where \( y \) is less than or equal to \( -2x + 1 \).<br /><br />Here is a step-by-step visual representation:<br /><br />- Plot the y-intercept (0, 1).<br />- From (0, 1), move right 1 unit and down 2 units to plot (1, -1).<br />- Draw a solid line through these points.<br />- Shade the region below the line.<br /><br />The final graph will show a solid line passing through (0, 1) and (1, -1), with the region below the line shaded.