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The Cartesian coordinate plane is a foundational concept in mathematics and is crucial for graphing ordered pairs. It's essentially a grid used to pinpoint the location of points using coordinates. Comprised of two perpendicular number lines, it is named after the mathematician René Descartes. The horizontal line is called the x-axis, and the vertical line is called the y-axis. These two axes intersect at a point known as the origin, marked by the coordinates (0,0).

When setting up a Cartesian plane, you'll often label axes to establish the scale. This helps to reliably map out the position of points. Keep in mind that each point on the plane corresponds to an ordered pair, reflecting its horizontal and vertical distances from the origin.

The x-coordinate is the first number in an ordered pair, providing the horizontal position of a point on the Cartesian coordinate plane. It indicates how far and in which direction to move from the origin along the x-axis. For example, in the ordered pair \((-3, \frac{5}{3})\), the x-coordinate is -3.

Here's what this means for graphing:

• If the x-coordinate is positive, move to the right of the origin.
• If the x-coordinate is negative, move to the left of the origin.

In our example, since -3 is negative, you will move 3 units to the left of the origin on the x-axis.

The y-coordinate is the second number in an ordered pair. It tells us about the vertical position on the Cartesian coordinate plane. This value shows how much to move up or down from the x-coordinate along the y-axis.

In the ordered pair \((-3, \frac{5}{3})\), the y-coordinate is \(\frac{5}{3}\). Here's a simple way to handle it:

• If the y-coordinate is positive, move upwards from the x-coordinate.
• If the y-coordinate is negative, descend downwards starting from the x-coordinate.

In this scenario, since \(\frac{5}{3}\) is positive, you will extend \(\frac{5}{3}\) units upwards from the point marked by the x-coordinate.

Plotting points on a Cartesian coordinate plane is like joining the dots. It's the process of marking the location where the x and y coordinates intersect. Once you have moved horizontally and vertically based on the ordered pair values, you'll place a dot at that intersection point.

Let's break down the action steps:

• Start at the origin (0,0).
• Move horizontally according to the x-coordinate.
• Move vertically according to the y-coordinate.
• Place a dot where the final position lies.

For the ordered pair \((-3, \frac{5}{3})\), after moving 3 units left on the x-axis and then \(\frac{5}{3}\) units up, the point you'll plot will accurately represent those coordinates on the graph.