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A vertical line is a line that goes straight up and down on the Cartesian plane. The defining feature of vertical lines is that they have a constant x-coordinate and their slope is undefined. These lines are parallel to the y-axis.

For example, in the equation x=4, the x-coordinate is always 4. This means every point on this vertical line has an x value of 4 while the y value can be any number. To graph this line, you simply find points where x equals 4 (like (4,0) and (4,1)), and then draw a line through these points.

The Cartesian plane is a two-dimensional surface made up of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). These axes intersect at a point called the origin, labeled as (0,0). This system allows us to represent points and graph equations.

Points on the plane are represented as coordinates (x, y), where x indicates the position along the horizontal axis and y indicates the position along the vertical axis. For example, the point (4,2) is located 4 units to the right of the origin and 2 units up.

When plotting equations like x=4, the Cartesian plane helps us visualize how all the points with a specific x-coordinate (but any y-coordinate) form a vertical line.

Plotting points involves locating specific points on the Cartesian plane using their coordinates. The x-coordinate tells you how far to move horizontally, and the y-coordinate tells you how far to move vertically.

For example, to plot the point (4,0), start at the origin (0,0), move 4 units to the right to position yourself at (4,0) and don't move up or down since the y-coordinate is 0. Then, plot another point like (4,1) by moving 1 unit up from (4,0).

By marking multiple points that follow this rule and then connecting them, you can graph a line, in this case, a vertical line for the equation x=4.