Lesson 5.7

Slope-Intercept Form

The most famous equation in algebra. It tells you exactly where to start and exactly where to go.

Introduction

You've learned about Slope (). Now we meet its partner, the Y-Intercept (). Together, they form the superpower equation that lets you graph any line in seconds without a table.

Past Knowledge

Lesson 5.5 (Direct Variation). Those lines () explain the slope part. Now we add the starting point.

Today's Goal

Identify the Slope () and Y-Intercept () from the equation .

Future Success

This is the default format for lines in science, engineering, and graphing calculators.

Key Concepts

The Anatomy of a Line

y = mx + b

m = Slope

How it Moves.

Rise / Run

b = Y-Intercept

Where it Begins.

Crosses the Y-axis (0, b)

Worked Examples

Example 1: Identify Parts

Basic

Find the slope and y-intercept.

Slope ()

The number attached to .

Y-Intercept ()

The number by itself.

Example 2: Tricky Signs

Intermediate

Find and . Include the signs!

Slope ()

Slope is negative.

Y-Intercept ()

We are subtracting 3, so is negative.

Example 3: Invisible Numbers

Advanced

Identify and for .

Hidden 1

is really .

Hidden 0

There is nothing added.

Common Pitfalls

The "x" isn't part of slope

If , the slope is 3, NOT . Slope is a number. is the input variable.

Wrong Order

is not in standard order. Slope is attached to (), not just the first number. Rewrite it as .

Real-Life Applications

Taxi Fares: An Uber might charge $5 to pick you up (, the starting fee) and $2 per mile (, the rate). The equation is . This format lets you instantly see the base cost and the running cost.