Lesson 6.1

Writing Equations from a Graph

A graph is just a picture of an equation. Your job is to translate that picture back into algebra.

Introduction

You already know how to graph a line if we give you the equation. Now we reverse it. We give you the line, you find the .

Past Knowledge

Lesson 5.2 (Finding Slope from a Graph). You already know how to count Rise over Run.

Today's Goal

Identify the y-intercept (), calculate slope (), and write the equation.

Future Success

This visual skill is crucial for standardized tests and physics labs.

Key Concepts

The Two-Step Method

b

Step 1: Find b (Begin)

Look at the Y-axis (the vertical one). Where does the line cross it? That number is your y-intercept, .

Example: Crosses at 3? .

m

Step 2: Find m (Move)

Start at the y-intercept. Pick another clear point on the line. Count the steps to get there.

Worked Examples

Example 1: Positive Slope

Basic

Find the equation of the line.

Step 1: Find b

The line crosses the y-axis at 1.

Step 2: Find m

Start at (0,1). To get to the next point (1,3), we go UP 2 and RIGHT 1.

Example 2: Negative Slope

Intermediate

Find the equation of the line.

Step 1: Find b

The y-intercept is at positive 3.

Step 2: Find m

From (0,3) to (2,2). We go DOWN 1, RIGHT 2.

Example 3: Through the Origin

Advanced

Find the equation.

Step 1: Find b

It goes right through the center (Origin).

Step 2: Find m

Up 3, Right 1.

We don't write "+ 0".

Common Pitfalls

Run over Rise?

Slope is always . Students often flip it because we read left-to-right (horizontal first). Slope measures Vertical steepness first.

Missing the Negative

If the line goes DOWN from left to right, your slope MUST be negative. Check this every time before you finish.

Real-Life Applications

Science Labs: In physics, you measure data points and plot them. The line of best fit tells you the relationship.

For example, plotting Distance vs. Time:

  • The y-intercept () is your starting position.
  • The slope () is your speed (velocity).

You can tell how fast something is moving just by looking at the steepness!

Practice Quiz

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