1. The Coordinate Plane as a Data Map

The coordinate plane is a precise map for numerical relationships. The horizontal axis is the x-axis, the vertical axis is the y-axis, and their crossing point is the origin, \((0,0)\).

Every point is written as an ordered pair:
\[ (x,y). \]
The first number tells how far to move left or right. The second number tells how far to move up or down.

Quadrant signs are predictable:

• Quadrant I: \(x>0,\ y>0\)
• Quadrant II: \(x<0,\ y>0\)
• Quadrant III: \(x<0,\ y<0\)
• Quadrant IV: \(x>0,\ y<0\)

Points on an axis are not inside any quadrant. A point with \(x=0\) lies on the y-axis, and a point with \(y=0\) lies on the x-axis.

Common misconception: reversing the order. The point \((3,-2)\) means 3 right and 2 down, not 3 up and 2 right.

Academic habit: read coordinates aloud as "across, then up or down." This prevents most coordinate-order mistakes.