Slope and the Equation of a Line

Learn slope, slope-intercept form, and equation of lines. Grade 9 Alberta mathematics curriculum.

Lesson 4.3 of Linear Equations in Grade 9 Math — Alberta curriculum lessons.

What you'll learn in this lesson

• Slope of a Line. Learn what slope means and how it shows how steep or flat a line is.
• Calculating Slope from a Graph or Table. Find the slope by comparing how much y changes for every change in x.
• Slope-Intercept Form (y = mx + b). Understand what m and b represent in a linear equation and how to write one.
• Horizontal and Vertical Lines. See what happens when slope is zero or undefined and how those lines look.

Inside the lesson — a free preview

What Are Oblique Lines?

📐 Oblique Lines. An oblique line is a slanted line — it isn't horizontal (flat) or vertical (straight up and down).

📈 Two Types of Oblique Lines.

What Is Slope?

🟦 Understanding Slope. The slope tells us how steep a line is — or how much it rises or falls as you move across the graph.

💡 Remember.

Slope Formula

🟨 The Slope Formula. The slope of a line is found using:

m = rise ÷ run

📝 Where:.

🟨 Using Two Points. If you have two points, (x₁, y₁) and (x₂, y₂):

m = (y₂ - y₁) ÷ (x₂ - x₁)

💡 Note. This formula gives the slope between any two points on the line.

Understanding Rise and Run

🧭 How to Count Rise and Run. When moving from one point to another on a line:

Then divide rise ÷ run..

📝 Example: From (1, 2) to (3, 6). Using the formula: m = (y₂ - y₁) ÷ (x₂ - x₁)

Comparing Lines with Different Slopes

🟧 Line Comparison. Here's how different slope values affect the line:

🟩 Two Ways to Find Slope

Comparing the Methods. The slope of a line shows how much the line rises or falls as you move across. We can find slope in two ways — both mean the exact same thing:

Method 1: m = rise ÷ run (Graph Method)Method 2: m = (y₂ - y₁) ÷ (x₂ - x₁) (Formula Method)

🟦 Method 1: Using Rise and Run (Graph Method)

When to Use This. When you have a graph, you can see the slope by counting squares on the grid.

Steps.

📝 Example: Points (1, 2) and (4, 8).

✅ The slope is 2. The line rises 2 units for every 1 unit across.

Worked example: Fractional Slope

Find the slope through (1, 2) and (5, 4).

Using the Formula.

✅ The slope is ½. The line rises slowly — up 1 unit for every 2 units across.

💡 Understanding Fractional Slopes.

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