91Ó°ÊÓ

A horizontal line is a straight line that runs from left to right across the coordinate plane. These lines have a slope of zero because they do not rise or fall as they move horizontally. The equation of a horizontal line is always in the form \( y = k \), where \( k \) is a constant. This means that the y-coordinate remains constant while the x-coordinate can take any value.
For example, in the problem, the equation \( y = 1 \) specifies that the y-coordinate is always 1 regardless of the x-coordinate. This results in a line parallel to the x-axis passing through all points where \( y = 1 \).
Another common example would be the line given by the equation \( y = -2 \), which would run parallel to the x-axis through points like (0, -2) and (5, -2). The key idea is that no matter what the x-value is, the y-value remains constant for horizontal lines.

Graphing equations is a visual way to represent relationships between variables. For a linear equation such as \( y = 1 \), graphing involves plotting points that satisfy the equation and then drawing a line through these points.
To graph \( y = 1 \):
1. Identify that it's a horizontal line, meaning \( y \) stays at 1 while \( x \) can be any number.
2. Choose several values for \( x \), like -3, 0, and 2.
3. Plot the points (-3, 1), (0, 1), and (2, 1) on the coordinate plane.
4. Draw a straight line through these points, making sure it extends across the entire plane parallel to the x-axis.
Graphing solidifies understanding of equations by translating abstract concepts into concrete visuals. It's a foundational skill for understanding more complex functions and datasets.

The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It consists of a horizontal axis called the x-axis, and a vertical axis called the y-axis. The point where these axes intersect is known as the origin, denoted by (0, 0).
Each point on the plane is represented by a pair of numbers (x, y). The first number is the x-coordinate, which shows the position relative to the y-axis. The second number is the y-coordinate, which shows the position relative to the x-axis.
For example, in the equation \( y = 1 \), plotting points involves selecting various x-values and using the constant y-value of 1. Points like (-3, 1), (0, 1), and (2, 1) are plotted, showing that the y-coordinate remains constant at 1 across the coordinate plane.
Understanding the coordinate plane is crucial for graphing equations, as it provides the framework to plot and visualize relationships between variables in a systematic way.