Lesson 6.10

Parallel Lines

Like railroad tracks, parallel lines go in the exact same direction and never touch. In Algebra, "same direction" means "same slope".

Introduction

If two lines have different steepness, they will eventually cross. If they have the exact same steepness, they will run side-by-side forever.

Past Knowledge

Lesson 5.7 (Slope-Intercept Form). You need to be able to find in an equation.

Today's Goal

Understand that parallel lines have .

Future Success

This concept is crucial in Geometry for proving properties of quadrilaterals (parallelograms, rectangles).

Key Concepts

The Golden Rule

Parallel Lines have the SAME SLOPE.

Line 1

Line 2

The must be identical. The must be different.

Worked Examples

Example 1: Identification

Basic

Are these lines parallel?

Line A:
Line B:

Yes.

Both have slope .

Example 2: Writing Equations

Intermediate

Write an equation for a line parallel to passing through .

Step 1: Steal the Slope

Old line has .

Our new line must also have .

Step 2: Use Point-Slope Form

Use and point .

Example 3: Tricky Format

Advanced

Write a parallel line to through .

Step 1: Find the Slope First!

The slope is NOT 2. We must convert to .

. So .

Step 2: Write Equation

Common Pitfalls

Assuming Slope

In , students often guess the slope is 2. It isn't! You always have to solve for first ().

Changing the Intercept

Sometimes students find the correct parallel line , but then accidentally write because they were copying from the old line. Only copy the slope!

Real-Life Applications

Construction & Design:

Roof trusses must be parallel for stability.
Road lanes are parallel curves.
Programming video games: Moving a character "forward" means adding a velocity vector parallel to their facing direction.