Lesson 6.4

Writing Equations from Two Points

This is the "Boss Fight" of the chapter. You have to use every skill you've learned so far: finding slope, solving for b, and writing the equation.

Introduction

Sometimes you don't know the rate () OR the start (). You just have two pieces of data. "In year 1, profits were $50k. In year 3, profit were $90k." From just that, you can build the entire model.

Past Knowledge

Lesson 5.3 (Slope Formula). You MUST be able to calculate .

Today's Goal

Combine steps: Find first, THEN find .

Future Success

This is the most common way real-world models are built from raw data.

Key Concepts

The Full Process

  1. Calculate Slope ().
  2. Pick ONE point.

    It doesn't matter which one. Pick the easier numbers (positives, smaller numbers).

  3. Solve for .

    Plug into .

  4. Write the Equation.

Worked Examples

Example 1: Positive Slope

Basic

Find the line passing through and .

Step 1: Find Slope

Step 2: Solve for b

Pick .

Example 2: Negative Slope

Intermediate

Find the line passing through and .

Step 1: Find Slope

Step 2: Solve for b

Pick .

Add 8 to both sides.

Example 3: Horizontal Line

Advanced

Find the line passing through and .

Step 1: Find Slope

Step 2: Solve for b

Remember HOY (Horizontal, Zero slope, y=)

Common Pitfalls

Arithmetic Errors

Slope formula involves subtraction. If you have negative numbers, be careful! becomes . Double check your signs.

Order Matters (Sort of)

If you start with on top, you MUST start with on bottom. Don't criss-cross your points.

Real-Life Applications

Business Growth:

  • Year 1: 100 customers. Year 5: 500 customers.
  • Slope: customers per year.
  • You can now predict Year 10 just from those two points!

Practice Quiz

Loading...