Graph the inequality \(3x - y \leq 9\) on a coordinate plane.

To graph the inequality \(3x - y \leq 9\), we can follow these steps: 1. **Rewrite the inequality**: First, we can rewrite the inequality in slope-intercept form (i.e., \(y = mx + b\)): \[ -y \leq -3x + 9 \] Multiplying through by -1 (and flipping the inequality sign) gives: \[ y \geq 3x - 9 \] 2. **Graph the boundary line**: The boundary line is given by the equation \(y = 3x - 9\). To graph this line, we can find two points: - When \(x = 0\): \[ y = 3(0) - 9 = -9 \quad \text{(Point: (0, -9))} \] - When \(x = 3\): \[ y = 3(3) - 9 = 0 \quad \text{(Point: (3, 0))} \] Now, plot the points \((0, -9)\) and \((3, 0)\) on the coordinate plane. 3. **Draw the line**: Since the inequality is \(\leq\), we will draw a solid line through these points to indicate that points on the line are included in the solution set. 4. **Shade the appropriate region**: The inequality \(y \geq 3x - 9\) indicates that we want to shade the region above the line. This includes all points where the \(y\)-value is greater than or equal to the \(y\)-value on the line. 5. **Final graph**: The final graph will show a solid line representing \(y = 3x - 9\) and the region above this line shaded. Here’s a summary of the graphing steps: - Draw a solid line for \(y = 3x - 9\). - Shade the area above the line to represent the solution set for the inequality \(3x - y \leq 9\). This is how you would graph the inequality on a coordinate plane.