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A horizontal line is a straight line that extends from left to right on a graph. In the context of graphing equations, when the equation is of the form \( y = c \), where \( c \) is a constant, it means that for any given point on this line, the \( y \)-value is always \( c \). This is the defining property of a horizontal line.

- The slope of a horizontal line is zero, which means there's no vertical change as you move along the line.- In our equation \( y = -10 \), the horizontal line is specifically at \( y = -10 \) across all \( x \)-values.

The simplicity of a horizontal line makes it easy to graph because the \( y \)-value remains unchanged, providing a straightforward guideline to plot the line accurately.

Ordered pairs are a fundamental part of graphing. They describe the location of a point on the coordinate plane, formatted as \( (x, y) \). Each ordered pair shows:

- The \( x \)-coordinate, which tells where the point is horizontally.- The \( y \)-coordinate, which shows the vertical position.

For our example equation \( y = -10 \), regardless of our \( x \)-value, the \( y \)-value in each ordered pair is always \(-10\). Therefore, some example ordered pairs are:

• (0, -10)
• (1, -10)
• (2, -10)
• (3, -10)
• (4, -10)

These pairs help us plot specific points on the line to ensure the graph is precise.

The coordinate plane is a two-dimensional plane that allows us to graph equations visually. It consists of two intersecting lines: the horizontal x-axis and the vertical y-axis. Where these axes meet is called the origin, represented by the ordered pair \( (0, 0) \).

Key aspects of the coordinate plane include:

• Divided into four quadrants, with positive and negative values.
• The horizontal line shows where values increase or decrease along the x-axis.
• The vertical line shows changes in values along the y-axis.

For the equation \( y = -10 \), the line is plotted on this plane, always keeping \( y \) constant, which simplifies finding and marking each point.

In any equation or graph, understanding x-values and y-values is crucial. They determine the position and behavior of points on the graph.

- **X-values** refer to the horizontal position of a point. You can choose any x-value to create ordered pairs, especially when graphing a horizontal line.- **Y-values** define the vertical position of a point. In a horizontal line equation like \( y = -10 \), the y-value stays constant.

Interpreting Values

For graphing purposes:

• The x-values can vary widely to show the line's full reach across the plane.
• The y-value is fixed at \(-10\) in this example, defining the line's consistent horizontal position.

A firm grasp of x-values and y-values helps in accurately plotting and understanding any graph.