1. The problem involves understanding and plotting linear equations given in different forms, along with their corresponding points. 2. The general form of a linear equation is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 3. For equations not in this form, we can rearrange them to solve for $y$ or $x$ to identify slope and intercepts. 4. Let's analyze the first equation $y = -x$ and the given point $(-2, -2)$. 5. Substitute $x = -2$ into $y = -x$: $$y = -(-2) = 2$$ 6. The given point is $(-2, -2)$ but substituting $x = -2$ gives $y = 2$, so the point does not lie on the line $y = -x$. 7. This suggests a possible error in the table or a misunderstanding; however, the equation $y = -x$ means the line passes through points where $y$ is the negative of $x$. 8. For the second equation $x = -y$ and point $(7, -2)$: 9. Substitute $y = -2$ into $x = -y$: $$x = -(-2) = 2$$ 10. The point given is $(7, -2)$ but substituting $y = -2$ gives $x = 2$, so the point does not lie on the line $x = -y$. 11. For the third equation $y = 6x - 2$ and point $(-1, 1)$: 12. Substitute $x = -1$: $$y = 6(-1) - 2 = -6 - 2 = -8$$ 13. The point given is $(-1, 1)$ but substituting $x = -1$ gives $y = -8$, so the point does not lie on the line. 14. For the fourth equation $x = 4y$ and point $(-4, 4)$: 15. Substitute $y = 4$: $$x = 4(4) = 16$$ 16. The point given is $(-4, 4)$ but substituting $y = 4$ gives $x = 16$, so the point does not lie on the line. 17. For the fifth equation $2x - y = 8$ and points with $y = -10$ and $y = -6$: 18. Solve for $x$: $$2x - y = 8 \Rightarrow 2x = 8 + y \Rightarrow x = \frac{8 + y}{2}$$ 19. Substitute $y = -10$: $$x = \frac{8 + (-10)}{2} = \frac{-2}{2} = -1$$ 20. Substitute $y = -6$: $$x = \frac{8 + (-6)}{2} = \frac{2}{2} = 1$$ 21. For the sixth equation $x - 6y = 12$ and points with $y = -3$ and $y = -2$: 22. Solve for $x$: $$x = 12 + 6y$$ 23. Substitute $y = -3$: $$x = 12 + 6(-3) = 12 - 18 = -6$$ 24. Substitute $y = -2$: $$x = 12 + 6(-2) = 12 - 12 = 0$$ 25. For the last equation $y = 3x - 5$ and points with $y = -5$ and $y = -8$: 26. Solve for $x$: $$y = 3x - 5 \Rightarrow 3x = y + 5 \Rightarrow x = \frac{y + 5}{3}$$ 27. Substitute $y = -5$: $$x = \frac{-5 + 5}{3} = 0$$ 28. Substitute $y = -8$: $$x = \frac{-8 + 5}{3} = \frac{-3}{3} = -1$$ This analysis shows how to verify points on lines and rearrange equations to find missing values. Final answer: The points given in the tables do not all lie on their respective lines as per the equations provided, indicating possible errors or mismatches in the data.