Lesson 6.2

Writing Equations from Slope & Y-Intercept

This is the easiest lesson in the chapter. If you are given the ingredients, you just have to mix them.

Introduction

Sometimes, math problems just tell you the answer. If a problem says "Slope is 5, Y-intercept is 3", you don't need to calculate anything. You just need to know where to put the numbers.

Past Knowledge

Lesson 5.7 (Slope-Intercept Form). You learned that is the magic formula.

Today's Goal

Given and , simply write the equation .

Future Success

This is the foundation for word problems. "Rate" becomes , "Start" becomes .

Key Concepts

Just Plug It In

The formula has two empty slots:

y =

SLOPE

x +

Y-INT

Your only job is to replace the boxes with numbers.

Worked Examples

Example 1: Basic Substitution

Basic

Write an equation for a line with slope and y-intercept .

Step 1: Identify m and b

Slope , so .

Y-intercept , so .

Step 2: Plug into Formula

Example 2: Handling Negatives

Intermediate

Write an equation for a line with and .

Step 1: Plug into Formula

Wait! is just .

Example 3: Zero and One

Advanced

Slope is and y-intercept is .

Step 1: Initial Plug-in

Step 2: Clean Up

We don't write "", just "".

We don't write "", just leave it blank.

Common Pitfalls

Mixing them up

Students often put the slope where the y-intercept belongs. Remember: is for Move (Rate), is for Begin (Start).

Forgetting x

Don't write . The slope ALWAYS needs the variable next to it. .

Real-Life Applications

Uber/Taxi Fares:

The "Booking Fee" is your flat start fee. That's ($5.00).
The "Cost per Mile" is your rate. That's ($2.00/mile).

Equation: . If you know this, you can predict your fare.