1. **State the problem:** We are given the system of equations: $$9x + y = 28$$ $$x + y = -4$$ and a table of points to verify, plus we need to find the slope of the line. 2. **Find the solution for $x$ and $y$:** From the second equation, isolate $y$: $$y = -4 - x$$ Substitute into the first equation: $$9x + (-4 - x) = 28$$ Simplify: $$9x - 4 - x = 28$$ $$8x - 4 = 28$$ Add 4 to both sides: $$8x - \cancel{4} + \cancel{4} = 28 + 4$$ $$8x = 32$$ Divide both sides by 8: $$\frac{8x}{\cancel{8}} = \frac{32}{\cancel{8}}$$ $$x = 4$$ Substitute $x=4$ back into $y = -4 - x$: $$y = -4 - 4 = -8$$ So the solution is: $$X = (4, -8)$$ 3. **Verify the points in the table:** - For $x = -2$, $y = 9$ - For $x = 8$, $y = 11$ - For $x = 13$, $y = 12$ Check if these satisfy the first equation $9x + y = 28$: - $9(-2) + 9 = -18 + 9 = -9 \neq 28$ - $9(8) + 11 = 72 + 11 = 83 \neq 28$ - $9(13) + 12 = 117 + 12 = 129 \neq 28$ They do not satisfy the first equation, so these points are not on the line defined by the system. 4. **Find the slope of the line:** Rewrite the second equation as $y = -4 - x$ which is $y = -x - 4$. The slope-intercept form is $y = mx + b$, so the slope $m = -1$. **Final answers:** $$X = (4, -8)$$ Slope: $$-1$$