To determine which of the given sets of ordered pairs lie on the [tex]\( y \)[/tex]-axis of a coordinate grid, we need to consider the definition of the [tex]\( y \)[/tex]-axis. Specifically, a point lies on the [tex]\( y \)[/tex]-axis if and only if its [tex]\( x \)[/tex]-coordinate is zero.
Let's analyze each given ordered pair:
1. [tex]\((3, -1)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is 3.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.
2. [tex]\((0, -4)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is 0.
- Since the [tex]\( x \)[/tex]-coordinate is zero, this point lies on the [tex]\( y \)[/tex]-axis.
3. [tex]\((-3, 0)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is -3.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.
4. [tex]\((-4, 0)\)[/tex]:
- The [tex]\( x \)[/tex]-coordinate is -4.
- Since the [tex]\( x \)[/tex]-coordinate is not zero, this point does not lie on the [tex]\( y \)[/tex]-axis.
After analyzing each pair, we conclude that the only pair that lies on the [tex]\( y \)[/tex]-axis is [tex]\((0, -4)\)[/tex].
