1. **State the problem:** We need to determine which graph represents the inequality $$2x + 3y \leq 6$$. 2. **Rewrite the inequality in slope-intercept form:** Start with $$2x + 3y \leq 6$$. Subtract $$2x$$ from both sides: $$3y \leq 6 - 2x$$ Divide both sides by 3: $$y \leq \frac{6 - 2x}{3}$$ Show cancellation: $$y \leq \frac{\cancel{3} \times 2 - \cancel{3} \times \frac{2}{3}x}{\cancel{3}} = 2 - \frac{2}{3}x$$ So the inequality is: $$y \leq -\frac{2}{3}x + 2$$ 3. **Interpret the inequality:** The boundary line is $$y = -\frac{2}{3}x + 2$$. - The y-intercept is 2. - The slope is $$-\frac{2}{3}$$, meaning the line slopes downward. - The inequality $$y \leq -\frac{2}{3}x + 2$$ means the shaded region is **below or on** the line. 4. **Compare with the graphs:** - Graph A shows a line crossing the y-axis at 2 and the x-axis at 3 (since when $$y=0$$, $$0 = -\frac{2}{3}x + 2 \Rightarrow x=3$$). - The shaded region in Graph A is **above** the line, which corresponds to $$y \geq -\frac{2}{3}x + 2$$, not $$\leq$$. - Graph B shows a dashed line with y-intercept above 6 and x-intercept just below 6, so it does not match the line equation. - Graph C is similar to B but shades the region above and to the right, which also does not match. 5. **Conclusion:** The inequality $$2x + 3y \leq 6$$ corresponds to the line $$y = -\frac{2}{3}x + 2$$ with shading **below** the line. Graph A has the correct line but shades **above** it, so it does not represent the inequality. None of the other graphs match the line or shading. Therefore, **none of the graphs exactly represent $$2x + 3y \leq 6$$, but Graph A has the correct line equation.** If forced to choose, Graph A is the closest but with incorrect shading. Final answer: Graph A shows the correct boundary line for $$2x + 3y \leq 6$$ but the shading is incorrect (it should be below the line).