Inequality Graph 411Aa8

1. The problem is to understand and graph the inequality $x + y \geq -3$. 2. This inequality represents all points $(x,y)$ in the coordinate plane where the sum of $x$ and $y$ is greater than or equal to $-3$. 3. The boundary line is given by the equation: $$x + y = -3$$ This line divides the plane into two half-planes. 4. To graph the boundary line, find intercepts: - When $x=0$, $y = -3$. - When $y=0$, $x = -3$. 5. Plot points $(0,-3)$ and $(-3,0)$ and draw a straight line through them. 6. Since the inequality is $\geq$, the region above or on the line is included. 7. To check which side to shade, test a point not on the line, for example $(0,0)$: $$0 + 0 = 0 \geq -3$$ is true, so shade the side containing $(0,0)$. 8. The graph is a half-plane including the line $x + y = -3$ and all points above it. Final answer: The solution set is the half-plane $x + y \geq -3$ including the boundary line.