Matching Equations and Graphs

Connect linear equations to their graphs. Grade 9 Alberta mathematics with visual examples.

What you'll learn in this lesson

Matching Equations and Graphs. Learn how to recognize how slope and y-intercept affect a line’s position and shape.
Walkathon Example. Use the fundraising graphs for Sam, Michael, and Ben to see how equations match real situations.

📐 Our Focus Equation. We're working with this equation:

y = 2x − 3

Slope-Intercept Form. This equation is written in slope-intercept form:

y = mx + b

Where:

From the equation y = 2x − 3:.

Slope (m).

Finding Slope on a Graph. You can find this slope on a graph by either:

Y-intercept (b).

When you look at the graph, check two things:.

1. Where the line crosses the y-axis.

2. How steep the line is.

Visual Characteristics.

✅ Verification. These points (0, −3), (1, −1), and (2, 1) should all lie on the same straight line.

🚶‍♂️ The Charity Walk. Ben, Michael, and Sam are walking in a 5 km charity walk.

Each of them has a different way to collect donations from sponsors.

📊 The Three Equations. You are given three equations that represent how much money (M) each person raises, depending on the distance (d) they walk:

Variables in Our Equations.

Sam's Fundraising Plan.

Calculation for 5 km. So after walking 5 km, Sam earns:

M = 1(5) + 5 = 10 dollars

How to spot Sam's graph:.

Michael's Fundraising Plan.

Calculation for 5 km. For 5 km:

M = 2(5) + 3 = 13 dollars

How to spot Michael's graph:.

Ben's Fundraising Plan.

Calculation for 5 km. For 5 km:

M = 4(5) = 20 dollars

How to spot Ben's graph:.

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