Lesson 5.12

Horizontal and Vertical Lines

Some lines break the rules. They don't have a "mix" of x and y. They pick one direction and stick to it forever.

Introduction

Most lines are slanted (oblique). But sometimes, a line is perfectly flat like the horizon, or perfectly straight up and down like a wall. These lines have special equations that look "missing" something.

Past Knowledge

Lesson 5.1 (Types of Slope). You learned that Horizontal = 0 slope and Vertical = Undefined.

Today's Goal

Graph and write equations for Horizontal () and Vertical () lines.

Future Success

These are the boundaries for Domain and Range exercises in future chapters.

Key Concepts

HOY VUX

Memorize this nonsense word. It saves lives.

HOY

  • H Horizontal Lines
  • 0 Zero Slope
  • Y Equation is

VUX

  • V Vertical Lines
  • U Undefined Slope
  • X Equation is

Worked Examples

Example 1: Graphing y = -3

HOY

Graph .

Analysis

It says ... so think HOY.

Horizontal line.

Go to -3 on the Y-axis and draw a flat line.

Example 2: Graphing x = 4

VUX

Graph .

Analysis

It says ... so think VUX.

Vertical line.

Go to 4 on the X-axis and draw a line straight up/down.

Example 3: Writing Equations

Advanced

Write the equation of the horizontal line going through .

Step 1: Check HOY/VUX

"Horizontal" means HOY.

Equation starts with .

Step 2: Pick the Coordinate

The point is . The y-coordinate is 5.

The x-coordinate (2) doesn't matter! The line is at height 5 forever.

Common Pitfalls

The "Zero" Confusion

Horizontal lines have Zero Slope (). Vertical lines have NO Slope (Undefined). These are not the same thing. "0 dollars" is different from "Magic money that doesn't exist".

Axis Confusion

The X-axis itself is horizontal... but the equation is a VERTICAL line (the Y-axis). It's opposite.
is the X-axis (Horizontal).
is the Y-axis (Vertical).

Real-Life Applications

Game Design: "The floor is lava." The floor is a horizontal line (). If your character's y-position is less than 0, game over.

Walls: A wall in a video game is a vertical line (). You cannot move past .

Practice Quiz

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