Graphing on the Coordinate Plane

📍 Graphing on the Coordinate Plane

Part 1 of 5 — Meet the Coordinate Plane

Topics in This Part

🔑 Key Concept: A coordinate plane is just two number lines that cross. One goes across, one goes up — and together they let us name the exact location of any point with a pair of numbers.

The Two Number Lines

You already know a single number line — it counts $0, 1, 2, 3, \dots$ from left to right. A coordinate plane uses two of them:

• The $x$-axis is the horizontal line (it runs left-to-right, like the horizon).
• The $y$-axis is the vertical line (it runs up-and-down, like a flagpole).

The point where they cross is called the origin. The origin is the "home base" — it sits at $0$ on both axes.

💡 Memory trick: The letter x has a line you can lay flat — think "x is across." That leaves y for up.

Concept Check 🎯

The First Quadrant

When the two axes cross, they make four corners, called quadrants. In Grade 5 we work in just one of them — the first quadrant — where both numbers are zero or bigger.

Picture a grid in the corner of a page:

 y
 5 ·  ·  ·  ·  ·  ·
 4 ·  ·  ·  ·  ·  ·
 3 ·  ·  ·  ·  ·  ·
 2 ·  ·  ·  ·  ·  ·
 1 ·  ·  ·  ·  ·  ·
 0 ─────────────────  x
   0  1  2  3  4  5

• The numbers along the bottom count across — that's the $x$-axis.
• The numbers up the left side count upward — that's the $y$-axis.
• The origin $(0,0)$ sits in the bottom-left corner.

🔑 Key Idea: Every spot where a grid line crossing-point lands can be named by how far across and it is from the origin.

Label the Grid 🔽

Use what you just learned to finish each sentence about the grid above.

Count on the Axes 🧮

Look again at the grid above.

1) The numbers along the bottom ($x$-axis) go from $0$ up to what biggest number shown? 2) Starting at the origin, how many units would you climb up to reach the top of the grid (the highest number on the $y$-axis)?

You've Got the Map

You now know the parts of the coordinate plane:

• $x$-axis — the horizontal line (across)
• $y$-axis — the vertical line (up)
• Origin — the crossing point at $(0, 0)$

In Part 2 we'll learn how to write a point's address using two numbers — an ordered pair — and how to put a dot exactly where it belongs.

📍 Graphing on the Coordinate Plane

Part 2 of 5 — Ordered Pairs: An Address for Every Point

🔑 The Idea: A point's location is written as an ordered pair $(x, y)$. The order matters — the first number is always across, the second is always up.

What Is an Ordered Pair?

An ordered pair is two numbers inside parentheses, separated by a comma:

$(x, y) \quad\Longrightarrow\quad (\,\text{across},\ \text{up}\,)$

📍 Graphing on the Coordinate Plane

Part 3 of 5 — Reading Points Off a Graph

🔑 Why it works: Plotting puts a dot from a pair. Reading does the reverse — you find the pair from a dot by checking how far across and how far up it sits.

How to Read a Point

To name a point you see on the grid:

1. Drop straight down to the $x$-axis and read the number → that's your $x$-coordinate.
2. Slide straight left to the $y$-axis and read the number → that's your $y$-coordinate.

📍 Graphing on the Coordinate Plane

Part 4 of 5 — Distances, Paths & Patterns

🔑 Big Payoff: Once points have addresses, we can do math with them — measure how far apart two points are and spot patterns when points line up.

Distance Along a Grid Line

When two points share the same $y$-coordinate, they sit on the same horizontal line. To find the distance between them, subtract their $x$-coordinates.

Example: Distance from $(2, 3)$ to $$

📍 Graphing on the Coordinate Plane

Part 5 of 5 — Real-World Maps & Mastery Check

You can now (1) name the parts of the plane, (2) write and plot ordered pairs, (3) read points off a grid, and (4) measure distances and find patterns. Let's use it all on a real map.

A City Map on a Grid

Maps use coordinates all the time. Here is a tiny town where each block is one unit. The origin $(0,0)$ is the bus stop.