The Cartesian plane is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates. These coordinates are typically noted as [tex]\((x, y)\)[/tex]. The horizontal axis is known as the x-axis, and the vertical axis is known as the y-axis.
1. The horizontal axis is the one that goes from left to right. By convention, this is called the x-axis.
2. The vertical axis is the one that goes from bottom to top. By convention, this is called the y-axis.
Given the options:
- [tex]$x, y$[/tex]
- [tex]$y, x$[/tex]
- [tex]$y-x, x-y$[/tex]
- [tex]$x-y, y-x$[/tex]
We need to select the one where the first axis mentioned is horizontal and the second is vertical, in the conventional order.
- [tex]$x, y$[/tex]: This states that the horizontal axis is the x-axis and the vertical axis is the y-axis. This is correct.
- [tex]$y, x$[/tex]: This states that the horizontal axis is the y-axis and the vertical axis is the x-axis. This is incorrect.
- [tex]$y-x, x-y$[/tex]: These are expressions involving subtraction and do not directly correspond to the axes.
- [tex]$x-y, y-x$[/tex]: These are also expressions involving subtraction and do not directly correspond to the axes.
Thus, the correct answer where the horizontal axis is called the x-axis and the vertical axis is called the y-axis is:
[tex]$x, y$[/tex]
Therefore, the correct option is:
1. [tex]$x, y$[/tex]
