91Ó°ÊÓ

The x-axis is an essential part of the coordinate plane, serving as the horizontal line that runs from left to right. It forms the baseline against which vertical positions, or y-values, are measured.
By convention, the x-axis is where the value of y is always zero. Therefore, any point on the x-axis can be represented as - \(x, 0\)where x can be any real number.
In mathematical terms, the equation of the x-axis can be expressed as - \(y = 0\).
This equation tells us that no matter how far we move along the horizontal line, the height above or below is always zero.

The y-axis serves as the vertical component of the coordinate plane, running from the bottom upward. It is crucial for measuring horizontal positions or x-values.
On the y-axis, the x value is always zero, making any point on the y-axis signified as - \(0, y\)where y is any real number.
The equation representing the y-axis is - \(x = 0\).
This equation simply states that all points on the y-axis do not shift horizontally from the origin.

Equations of lines form the basis for graphing and understanding geometric relationships within a coordinate plane. Lines on this plane can be described using mathematical equations, which provide a precise way to understand their behavior.
A **horizontal line**, just like the x-axis, has an equation where y remains constant. For example, if a horizontal line passes through (0, 3), its equation would be \(y = 3\).
Similarly, a **vertical line**, akin to the y-axis, has an equation where x remains constant. For instance, if a vertical line goes through (4, 0), the line’s equation is \(x = 4\).
Understanding these equations can help you visualize how lines run parallel to the coordinate axes and why they intersect or remain distinct.

• Horizontal line: Constant y value (e.g., \(y = c\))
• Vertical line: Constant x value (e.g., \(x = c\))

These simple concepts are foundational in learning about more complex geometric and algebraic problems.