Which set of points lies on the graph of x = -2?(-2, 0), (-2, 2), (-2, -2)(0, -2), (2, -2), (-2, -2)(-2, 0), (2, -4), (-4, 2)

1. Break Down the Problem

We need to determine which points lie on the vertical line defined by the equation $x = -2$. For any point $(x, y)$ to lie on this line, the x-coordinate must be $-2$.

2. Relevant Concepts

The equation $x = -2$ describes a vertical line where all points on this line have an x-coordinate of $-2$. The y-coordinate can be any real number.

3. Analysis and Detail

Let's analyze each of the given points:

1. Point $(-2, 0)$ - x-coordinate is $-2$ ✔️
2. Point $(-2, 2)$ - x-coordinate is $-2$ ✔️
3. Point $(-2, -2)$ - x-coordinate is $-2$ ✔️
4. Point $(0, -2)$ - x-coordinate is $0$ ❌
5. Point $(2, -2)$ - x-coordinate is $2$ ❌
6. Point $(-2, -2)$ - x-coordinate is $-2$ ✔️
7. Point $(-2, 0)$ - x-coordinate is $-2$ ✔️ (Repeat)
8. Point $(2, -4)$ - x-coordinate is $2$ ❌
9. Point $(-4, 2)$ - x-coordinate is $-4$ ❌

4. Verify and Summarize

The points that have been verified to lie on the line $x = -2$ are $(-2, 0)$, $(-2, 2)$, and $(-2, -2)$.

Final Answer

The set of points that lie on the graph of $x = -2$ is: $(-2, 0)$, $(-2, 2)$, and $(-2, -2)$.