1. **State the problem:** We need to graph the inequality $$2x + 3y \geq -6$$ on the coordinate plane. 2. **Rewrite the inequality as an equation:** To graph the boundary line, convert the inequality to an equation: $$2x + 3y = -6$$ 3. **Find intercepts:** - For the x-intercept, set $$y=0$$: $$2x + 3(0) = -6 \implies 2x = -6 \implies x = \frac{-6}{2} = -3$$ - For the y-intercept, set $$x=0$$: $$2(0) + 3y = -6 \implies 3y = -6 \implies y = \frac{-6}{3} = -2$$ 4. **Plot the boundary line:** Plot points $$(-3,0)$$ and $$(0,-2)$$ and draw a straight line through them. 5. **Determine the shading region:** - Pick a test point not on the line, for example, the origin $$(0,0)$$. - Substitute into the inequality: $$2(0) + 3(0) = 0 \geq -6$$ which is true. - Since the test point satisfies the inequality, shade the region that includes the origin. 6. **Include the boundary line:** Because the inequality is $$\geq$$ (greater than or equal to), the boundary line is included and should be drawn solid. **Final answer:** The graph is the solid line through points $$(-3,0)$$ and $$(0,-2)$$ with the region above or on the line shaded, including the origin.