1. **Problem Statement:** We need to graph the linear inequality $$3x + y \leq -3$$ on the coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, express $y$ in terms of $x$. $$3x + y \leq -3 \implies y \leq -3 - 3x$$ 3. **Graph the boundary line:** The boundary line is the equation $$y = -3 - 3x$$ This is a straight line with slope $-3$ and y-intercept $-3$. 4. **Plot the boundary line:** - When $x=0$, $y = -3$ (point $(0,-3)$). - When $x=1$, $y = -3 - 3(1) = -6$ (point $(1,-6)$). Draw a solid line through these points because the inequality includes equality ($\leq$). 5. **Shade the solution region:** Since the inequality is $y \leq -3 - 3x$, shade the region below the line. 6. **Check a test point:** Use $(0,0)$ to verify. $$3(0) + 0 \leq -3 \implies 0 \leq -3$$ This is false, so do not shade the region containing $(0,0)$. 7. **Final graph:** Solid line for $y = -3 - 3x$ and shading below the line. This completes the graphing of the inequality.