Lesson 6.7

Converting Forms

Point-Slope form is great for writing equations, but Slope-Intercept form () is usually better for graphing. Let's learn how to switch between them.

Introduction

Converting is just simplifying. We start with the "messy" point-slope form and clean it up until is by itself.

Past Knowledge

Lesson 2.8 (Distribution). You must be able to distribute the slope into the parentheses.

Today's Goal

Turn into .

Future Success

This algebra manipulation skill is essential for solving systems of equations later.

Key Concepts

Two-Step Process

Start:

Step 1: Distribute

Multiply the slope by both terms inside.

Step 2: Isolate y

Move the constant from the left to the right.

Worked Examples

Example 1: Positive Numbers

Basic

Convert .

Step 1: Distribute

Step 2: Add 5

Example 2: Negative Slope

Intermediate

Convert .

Step 1: Distribute

Be careful: .

Step 2: Subtract 2

Example 3: Fraction Slope

Advanced

Convert .

Step 1: Distribute

Half of 6 is 3.

Step 2: Add 4

Common Pitfalls

Distributing Mistakes

Don't forget to multiply the slope by the SECOND number in the parenthesis. is , not .

Sign Errors

If you multiply a negative slope by a negative coordinate, the result is POSITIVE. becomes .

Real-Life Applications

Standardization:

  • In scientific fields, everyone usually agrees to publish final results in the same format () so they are easy to compare.
  • If Scientist A writes and Scientist B writes , it's hard to tell if they are the same.
  • Convert both: . Now we know they match!

Practice Quiz

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