1. **State the problem:** We are given the equation $y = 2$ and asked to analyze its graph and points related to it. 2. **Rewrite in standard form:** The equation $y = 2$ can be written as $0x + 1y = 2$. 3. **Make a table of values:** Choose four values for $x$ and find corresponding $y$ values. $$\begin{array}{c|c} x & y \\\hline -2 & 2 \\ 0 & 2 \\ 3 & 2 \\ 5 & 2 \end{array}$$ 4. **Plot points and graph:** The points $(-2,2)$, $(0,2)$, $(3,2)$, and $(5,2)$ lie on a horizontal line crossing the $y$-axis at $2$. 5. **Check if point $(2,8)$ lies on the line:** Substitute $x=2$, $y=8$ into $y=2$. $$8 \neq 2$$ So, $(2,8)$ does not lie on the line. 6. **Is $(2,8)$ a solution?** No, because it does not satisfy the equation. 7. **Check if point $(8,2)$ lies on the line:** Substitute $x=8$, $y=2$. $$2 = 2$$ So, $(8,2)$ lies on the line. 8. **Is $(8,2)$ a solution?** Yes, because it satisfies the equation. **Final answer:** The graph of $y=2$ is a horizontal line crossing the $y$-axis at $2$. Points with $y=2$ lie on the line; points with $y \neq 2$ do not.