Graph the inequality \(y \geq -2x + 4\) on a coordinate plane.

To graph the inequality \(y \geq -2x + 4\), follow these steps: 1. **Graph the boundary line**: First, we need to graph the line \(y = -2x + 4\). This line is the boundary of the inequality. - **Find the y-intercept**: Set \(x = 0\): \[ y = -2(0) + 4 = 4 \] So, the y-intercept is (0, 4). - **Find the x-intercept**: Set \(y = 0\): \[ 0 = -2x + 4 \implies 2x = 4 \implies x = 2 \] So, the x-intercept is (2, 0). - **Draw the line**: Plot the points (0, 4) and (2, 0) on the coordinate plane and draw a straight line through these points. Since the inequality is \(y \geq\), we will use a solid line to indicate that points on the line are included in the solution. 2. **Shade the appropriate region**: Since the inequality is \(y \geq -2x + 4\), we need to shade the region above the line. This represents all the points where \(y\) is greater than or equal to \(-2x + 4\). 3. **Check a test point**: To confirm the correct region is shaded, you can use a test point that is not on the line. A common choice is the origin (0, 0): \[ 0 \geq -2(0) + 4 \implies 0 \geq 4 \] This is false, so the region that includes (0, 0) should not be shaded. Therefore, the region above the line is indeed the correct area to shade. In summary, the graph consists of a solid line representing \(y = -2x + 4\) and the area above this line shaded to indicate the solution to the inequality \(y \geq -2x + 4\).