Understanding and Graphing Linear Relations

Master graphing linear relations on the coordinate plane. Grade 9 Alberta mathematics lesson.

Lesson 4.2 of Linear Equations in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

Inside the lesson — a free preview

The Cartesian Coordinate System

🟩 The Cartesian Coordinate System. The Cartesian plane helps us show how two quantities are related.

📏 The x-axis (Horizontal Line). The horizontal line is called the x-axis

📏 The y-axis (Vertical Line). The vertical line is called the y-axis

These two axes divide the plane into four quadrants:

💡 Remember. Each point on the plane is written as an ordered pair: (x, y).

Understanding Ordered Pairs

🟦 What is (x, y)?. A point consists of two coordinates: (x, y)

1️⃣ The First Number (x). The first number represents x — how far to move horizontally.

2️⃣ The Second Number (y). The second number represents y — how far to move vertically.

✅ Important Rule. X always goes first!

How to Plot a Point

🧭 Steps to Plot a Point.

What is a Linear Relation?

📐 Linear Relations. A linear relation shows a steady, consistent pattern between two quantities.

💼 Example: Hourly Earnings. You earn 15 for every hour you work.

✅ Why is this Linear?. Each hour, your money goes up by the same amount (+15) — that's what makes it linear.

Linear Graphs

📈 Linear Graphs. When we graph a linear relation, the points form a straight line.

✅ Linear Graphs.

❌ Non-Linear Graphs.

Discrete vs Continuous Graphs

🔵 Discrete vs Continuous Graphs. Some graphs show separate points, while others show a smooth line.

🔵 Discrete Data. Discrete data = values that are counted

🟢 Continuous Data. Continuous data = values that are measured

Worked example: s

📝 A: Plot (3, 2).

📝 B: Plot (−2, −4).

📝 C: Plot (−3, 5).

📝 D: Plot (4, −3).

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