Graphing on the Coordinate Plane

The Coordinate Plane

The coordinate plane is formed by two number lines that cross at the origin (0, 0):

• x-axis: The horizontal number line
• y-axis: The vertical number line

Ordered Pairs

A point is located by an ordered pair $(x, y)$:

• $x$ = how far right (horizontal)
• $y$ = how far up (vertical)

Example: $(3, 5)$ means go right 3 and up 5.

Plotting Points

To plot $(4, 2)$:

1. Start at the origin $(0, 0)$
2. Move right 4 along the x-axis
3. Move up 2 from there
4. Mark the point

The Origin

$(0, 0)$ is where the axes cross. It's the starting point for all plotting.

Practice Points

| Point | x | y | Description | |-------|---|---|-------------| | $A = (1, 3)$ | 1 | 3 | Right 1, up 3 | | $B = (4, 0)$ | 4 | 0 | Right 4, on x-axis | | $C = (0, 5)$ | 0 | 5 | On y-axis, up 5 | | $D = (2, 2)$ | 2 | 2 | Right 2, up 2 |

Patterns on the Coordinate Plane

Plotting number pattern pairs creates shapes and lines:

• $(1, 2), (2, 4), (3, 6), (4, 8)$ → makes a straight line (rule: $y = 2x$)

Real-World Uses

Maps use a grid system just like the coordinate plane! "Meet me at the corner of 3rd Street and 5th Avenue" is like saying $(3, 5)$.

Memory trick: Think of it as a house: you walk across the floor first (x), then climb the stairs (y). "Run before you rise!"