Back To Course

Math 101: College Algebra12 chapters | 94 lessons | 11 flashcard sets

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Elizabeth Foster*

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!

In this lesson, you'll take a look at some oddball slopes. But first, let's review the basics. **Slope** is the amount of vertical change per unit of horizontal change. In other words, as a line moves one unit to the right, how many units does it go up or down?

You learned in another lesson that if a line goes up from left to right, its slope is positive, and if it goes down from left to right, its slope is negative. You also know how to identify whether the slope is positive or negative when the line is written in *y* = *mx* + *b* form. *M* represents the slope of the line, so if *m* is positive, the slope is positive, and the line will be slanting upwards. If *m* is negative, the slope is negative, and the line will be slanting downwards.

But what if you get one of these?

In this lesson, you'll learn how to deal with both of those cases. They might look tricky when you first start out, but they're not actually that bad once you get to know them - in fact, they're some of the easiest slopes to handle!

First, we'll start with this one.

If the line is vertical, it means that the slope is **undefined**: it has no value that we can express in numbers. That's a pretty crazy concept, so let's take a look at what's going on here. You know that as a line gets steeper and steeper, the slope gets bigger and bigger if it's positive, or smaller and smaller if it's negative. In both cases, the absolute value of the slope increases as it gets steeper.

The bigger a number gets, the steeper the slope is. But the problem with numbers is that they can just keep getting bigger and bigger. There's no such thing as the biggest number. So, no matter how steep the slope is, there will always be a slope that's even steeper. You can just add or subtract 1.

To get a completely vertical slope, you'd have to have a number that was simultaneously the biggest and the smallest number in existence, but that's not possible. Neither of those numbers exist, and they certainly can't be the same number. That's why the slope is undefined. Mathematically, the slope isn't actually a real number; hence we call it undefined.

So if *m* is undefined, how do we write this line as an equation? If you look more closely at the graph, you'll see that the x-value is exactly the same for the entire line. So to represent this line numerically, we use the equation *x* = ____. The line here is the line *x* = -2. The x-value is the same for every value of y: it's always -2.

Now let's look at a similar problem: what about a horizontal line? As a line gets flatter and flatter, the absolute value of the slope gets smaller and smaller. But unlike the increasing slopes, there is a limit to how much a number can decrease. There is such a thing as a number with the smallest absolute value: 0.

That's why slope of a horizontal line is 0. You can also think of this mathematically. Slope represents how many units the line goes up for every unit it moves to the right. This line doesn't go up at all, so it goes up 0 units for every 1 unit of movement to the right. That makes the slope 0/1, or 0.

If we plug this into the *y* = *mx* + *b* form, we get *y* = 0*x* + *b*. Since any number multiplied by 0 is 0, we represent this line with the equation *y* = ____. Another way of looking at this is to notice that the value of y is always the same.

In this lesson, you learned about the slopes of horizontal and vertical lines. Vertical lines have an undefined slope, and they're written in the form *x* = ___. Horizontal lines have a slope of 0, and they're written in the form *y* = ___.

These slopes look a little complicated when you first approach them, but once you understand the concept behind them, they're really not that hard. They rely on all the same concepts that you learned about for normal slopes; they're just the very extremes of what can possibly happen. Now try out some for yourself on the quiz questions!

By working your way through this lesson, you should feel confident completing the following tasks:

- Recall the definition for the slope of a line
- State and explain the slopes of horizontal and vertical lines

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
6 in chapter 1 of the course:

Back To Course

Math 101: College Algebra12 chapters | 94 lessons | 11 flashcard sets

- What are the Different Types of Numbers? 6:56
- What Are the Different Parts of a Graph? 6:21
- What is a Linear Equation? 7:28
- Linear Equations: Intercepts, Standard Form and Graphing 6:38
- Abstract Algebraic Examples and Going from a Graph to a Rule 10:37
- Graphing Undefined Slope, Zero Slope and More 4:23
- What is a System of Equations? 8:39
- How Do I Use a System of Equations? 9:47
- Go to Foundations of Linear Equations

- Go to Functions

- Influence & Persuasion for Front-Line Managers
- Purpose-Driven Business Leadership
- Lean-Agile Mindset for Leaders
- Reducing Stress for Supervisors
- Team Building Skills for Supervisors
- Designing Influential Messages in Business
- Aligning Jobs, Goals, Purpose & Agenda
- Continuous Lean Process Improvement
- Overcoming Obstacles to Influence & Persuasion in Business
- Techniques & Tools for Influence in Business
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists

- Human Resources Management for Hospitality
- Willowbrook Hepatitis Experiments: Bioethics Case Study
- The Full Cycle of Event Planning in a Hotel
- The Electrical Stimulation Method: Theorists, Research & Applications
- Higher-order Determinants Lesson Plan
- Using Anecdotes to Persuade an Audience
- What Are Civil Disturbance Operations?
- Value Creation in Business: Definition & Example
- Quiz & Worksheet - Angles in Standard Position
- Quiz & Worksheet - Sustainable Tourism
- Quiz & Worksheet - Rhetorical Devices in In Cold Blood
- Quiz & Worksheet - Personalistic & Naturalistic Theory in Science
- Quiz & Worksheet - Synopsis of Wonder by R.J. Palacio
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- Art 101: Art of the Western World
- Understanding the Effects of Globalization in Business
- Supervision: Skills Development & Training
- Business Writing: Help & Review
- MTTC Mathematics (Secondary): Practice & Study Guide
- Bacterial Skin and Wound Infections: Help and Review
- Biochemistry in Anatomy and Physiology: Help and Review
- Quiz & Worksheet - How Visuals Impact Communication
- Quiz & Worksheet - The War of Austrian Succession
- Quiz & Worksheet - Self-Efficacy & Self-Monitoring in Organizations
- Quiz & Worksheet - Statute of Frauds Under the UCC
- Quiz & Worksheet - Oral, Written, Visual & Electronic Communication

- Using Visuals to Present Data: Textual Graphics vs. Visual Graphics
- Optic Nerve Damage: Causes, Symptoms & Treatment
- Journal Writing Prompts
- How to Pass the ASVAB
- How to Use the GED RLA Prep Course
- Creative Writing Exercises for Middle School
- Introduction to Geometry Lesson Plan
- Civil Rights Lesson Plan
- Homeschool Field Trip Ideas
- Summarizing Lesson Plan
- 5th Grade Persuasive Writing Prompts
- Next Generation Science Standards Appendix F

Browse by subject