A Cartesian plane is a flat grid formed by two number lines that cross at a right angle: the x-axis (horizontal) and the y-axis (vertical). Together, they let you locate any point using an ordered pair of numbers.

It is widely used in algebra, geometry, graphs, science, engineering, and everyday problem-solving.

• x-axis: the horizontal number line (left/right)
• y-axis: the vertical number line (down/up)
• origin: the point where the axes cross, written as (0, 0)

Positive numbers go right (x) and up (y). Negative numbers go left (x) and down (y).

A point on the Cartesian plane is written as an ordered pair: (x, y).

• x tells you how far to move left/right from the origin
• y tells you how far to move down/up from the origin

Always move x first, then move y.

• (3, 2): move 3 right, then 2 up
• (-4, 1): move 4 left, then 1 up
• (2, -5): move 2 right, then 5 down
• (0, 6): x is 0, so the point is on the y-axis
• (-7, 0): y is 0, so the point is on the x-axis

• Quadrant I: x positive, y positive → (+, +)
• Quadrant II: x negative, y positive → (-, +)
• Quadrant III: x negative, y negative → (-, -)
• Quadrant IV: x positive, y negative → (+, -)

Points on the axes are not in any quadrant.

1. Start at the origin (0, 0).
2. Move left/right to match the x value.
3. From there, move down/up to match the y value.
4. Mark the point and label it (optional).

• Mixing up x and y (remember: x comes first)
• Forgetting negative signs (left/down are negative)
• Putting axis points into a quadrant (they don’t belong to any quadrant)
• Counting the origin as 1 (the origin is 0)

• Graphing lines and curves (like y = 2x + 1)
• Understanding slope and intercepts
• Geometry: distance, midpoint, transformations
• Real-world graphs: speed vs time, cost vs quantity