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The coordinate plane is a two-dimensional space formed by two perpendicular lines called axes. The horizontal line is the x-axis, while the vertical line is the y-axis. Where these two lines meet is called the origin, with coordinates (0,0).

The coordinate plane allows us to place points in terms of their x (horizontal) and y (vertical) positions. A point on this plane is denoted as \(x, y\), where \(x\) represents the distance along the x-axis and \(y\) shows the distance along the y-axis. These axes are often marked with an equal scale for both positive and negative directions.

• The x-axis is horizontal and runs left and right.
• The y-axis is vertical and runs up and down.
• Every point on the plane can be identified by a set of coordinates (x, y).

The coordinate plane is essential for graphing linear equations, as it provides a visual way to connect algebra with geometry. In this exercise, we use the coordinate plane to help visualize and sketch the vertical line \(x = -2\) and horizontal line \(y = 2\). By plotting these lines, we can easily see where they meet, giving us the intersection point.

A vertical line on the coordinate plane is defined by an equation of the form \(x = a\), where \(a\) is a constant. This means every point on the line has the same x-coordinate. The line is parallel to the y-axis.
If we take the equation \(x = -2\), this represents a line where all points have an x-coordinate of -2. The y-coordinate can vary freely, which means the line extends infinitely up and down.

• This line is always parallel to the y-axis.
• Vertical lines have an undefined slope because division by zero in slope calculations (rise over run) is not possible.
• These lines do not cross the x-axis; instead, they are a constant distance from the origin on the x-axis.

To graph a vertical line like \(x = -2\), find \(-2\) on the x-axis, and draw a straight line through this point parallel to the y-axis. Such lines illustrate how the x-coordinate stays constant while the y-coordinate can be anything.

A horizontal line is shown by an equation of the form \(y = b\), where \(b\) is a constant, indicating that each point on the line has the same y-coordinate. This line runs parallel to the x-axis.
The equation \(y = 2\) tells us that at every point on this line, the y-coordinate is 2. The x-coordinate can vary, making the line stretch infinitely to the left and right.

• Horizontal lines are parallel to the x-axis.
• The slope of a horizontal line is zero because there is no vertical change (rise) over the horizontal change (run).
• These lines do not intersect the y-axis anywhere other than their constant value.

When graphing a horizontal line like \(y = 2\), find \2\ on the y-axis and draw a line parallel to the x-axis, which means it remains level and does not tilt. This representation shows how the y-coordinate is fixed while x can vary without restriction.