To determine which points can be used to create a line with an undefined slope through the point [tex]\((-3, 0)\)[/tex], we need to identify points that share the same x-coordinate as [tex]\((-3, 0)\)[/tex]. An undefined slope indicates a vertical line, which means all points on the line must have the same x-coordinate.
Let's analyze each given point:
1. [tex]\((-5, -3)\)[/tex]: This point has an x-coordinate of [tex]\(-5\)[/tex].
2. [tex]\((-3, -6)\)[/tex]: This point has an x-coordinate of [tex]\(-3\)[/tex].
3. [tex]\((-3, 2)\)[/tex]: This point has an x-coordinate of [tex]\(-3\)[/tex].
4. [tex]\((-1, 0)\)[/tex]: This point has an x-coordinate of [tex]\(-1\)[/tex].
5. [tex]\((0, -3)\)[/tex]: This point has an x-coordinate of [tex]\(0\)[/tex].
6. [tex]\((3, 0)\)[/tex]: This point has an x-coordinate of [tex]\(3\)[/tex].
We are looking for points with the same x-coordinate as the point [tex]\((-3, 0)\)[/tex]. The points that meet this criterion are:
- [tex]\((-3, -6)\)[/tex]
- [tex]\((-3, 2)\)[/tex]
Thus, the points that can be used to create a line with an undefined slope through [tex]\((-3, 0)\)[/tex] are:
[tex]\[
\boxed{(-3, -6) \text{ and } (-3, 2)}
\][/tex]
