Coordinates help us find a specific spot on a graph. It sounds tricky, but it’s actually pretty fun once you learn how to do it!

In the Cartesian plane, which has two crossed lines called axes, we use two numbers to explain a position. These numbers are known as the x-coordinate and the y-coordinate.

Here’s how it works:

1. Axes: The horizontal line is called the x-axis, and the vertical line is the y-axis. They cross each other at a point called the origin, which is shown as $(0, 0)$.

2. Coordinates: A point on the graph is written as an ordered pair $(x, y)$. This means:

   • The $x$ tells you how far to go left or right from the origin.
   • The $y$ tells you how far to go up or down from the origin.

3. Quadrants: The Cartesian plane is split into four sections, called quadrants, based on the signs of the coordinates:

   • Quadrant I: $(+,+)$ – both numbers are positive.
   • Quadrant II: $(-,+)$ – the first number is negative, the second is positive.
   • Quadrant III: $(-,-)$ – both numbers are negative.
   • Quadrant IV: $(+,-)$ – the first number is positive, the second is negative.

To plot a point, you start at the origin. First, move along the x-axis to the $x$ value. Then, move up or down to the $y$ value. It’s just like following a treasure map!

Once you’ve plotted a few points, you can connect them to create lines or shapes that show functions. Knowing about coordinates is super helpful because it helps us see how different numbers relate to each other. This makes graphs come to life!