Back To Course

NY Regents Exam - Geometry: Tutoring Solution10 chapters | 118 lessons

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

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Kimberlee Davison*

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

The slope-intercept form of the equation of a line is a useful form for graphing as well as for understanding the relationship between x and y. In this lesson, learn how the slope-intercept form helps you understand the equation of a line.

The equation of a line can be written many different ways, and each of these ways is valid. The **slope-intercept** form of a line is a way of writing the equation of a line so that the slope of the line and the *y*-intercept are easily identifiable. The **slope** is the steepness of the line, and the ** y-intercept** is the place the line crosses the

A line is a relationship between two things - but not just any relationship. When you have a **linear** relationship, one that can be graphed as a line, there is one big condition:

No matter how much you have of a thing (often called *x*), if you add one more you always get a consistent amount more of the other thing (often called *y*).

Let's look at some examples of linear relationships:

- The amount of pie you eat and the number of calories you consume: If each slice of pie has 400 calories, and you eat one more piece, you will have consumed 400 more calories. It is totally irrelevant how many pieces you have already eaten.
- The number of steps you take (of consistent size) and the distance you travel: If you take 100 more steps, and you can travel 1.5 feet with each step, then you have traveled 150 more feet, regardless of how far you've already walked.

It's important to know that all relationships are not linear. For example, the number of dogs you have and the amount of dog poop you have to clean up in the backyard is not linear. Some dogs make bigger messes than others.

This investigation of linear relationships has a purpose: to help you understand that a line (linear relationship) always suggests that increasing *x* a certain amount has a constant effect on *y*.

Let's return to the pie example. Every time you eat one more slice, you get 400 calories (assuming all the slices are the same size). So, if you eat two slices, you get 800 more calories (2 * 400). If you eat 3 slices, you get 1200 more calories (3 * 400). This amount more you get if you have 1 more of something when a relationship is linear is called the slope.

For our pie example, pretend for a moment that pie was all you ate for dinner. Call the number of slices you ate *x*. If you ate 2 slices, *x* = 2. If you ate 9 slices, *x* = 9. In each case, the number of calories you ate is *y*. How do you get from pie slices to calories? You multiply, like this: *y* = 400*x*

This is just the algebraic way of writing: Calories = 400 * Number of slices

Just by glancing at the equation *y* = 400*x* you can tell the slope of the line is 400. It is the amount *y* increases if *x* increases by one.

Now let's pretend that you didn't just eat pie for dinner. Maybe you had roast beef and potatoes, totaling 640 calories. You have to add that 640 calories to your total calorie consumption. Your total calories is still *y*, and your number of pie slices is still *x*. You aren't really sure how many slices you will eat yet. But no matter how much pie you eat, you will have to add 640 calories to it. By adding 640 to the previous equation you get: *y* = 400*x* + 640

The equation *y* = 400*x* + 640 is in slope-intercept form because we can look at it and immediately see the slope and the *y*-intercept. Usually, this form is described as ** y = mx + b** form.

Graphing is very simple if the line is written as *y* = *mx* + *b*. First, you identify the *y*-intercept, the place where the line crosses the *y*-axis (the thicker vertical line) and draw it as a point on the graph.

For example, suppose you have the line *y* = 3*x* + 1. The *y*-intercept is at *y* = 1, as shown in the picture.

Next, you use the slope to help you draw the correct steepness of the line. In this case, the slope is 3.'So, *y* increases by 3 every time *x* increases by 1. From the *y*-intercept, move in the *x*-direction 1 unit, go up 3 units and make a second point, as shown in the picture.

Once you have two points, drawing in the line is easy.

While the slope-intercept form of a line isn't the only way an equation of a line can be written, you will probably find that it is easy to understand and easy to graph - and a very useful way to understand the relationship between many things.

The **slope-intercept form** is simply the way of writing the equation of a line so that the **slope** (steepness) and ** y-intercept** (where the line crosses the vertical

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 79 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.

Back To Course

NY Regents Exam - Geometry: Tutoring Solution10 chapters | 118 lessons

- Triangles: Definition and Properties 4:30
- Area of Triangles and Rectangles 5:43
- Classifying Triangles by Angles and Sides 5:44
- Perimeter of Triangles and Rectangles 8:54
- Interior and Exterior Angles of Triangles: Definition & Examples 5:25
- How to Identify Similar Triangles 7:23
- Triangle Congruence Postulates: SAS, ASA & SSS 6:16
- Applications of Similar Triangles 6:23
- Congruence Proofs: Corresponding Parts of Congruent Triangles 5:19
- Perpendicular Bisector Theorem: Proof and Example 6:41
- Angle Bisector Theorem: Proof and Example 6:12
- Congruency of Isosceles Triangles: Proving the Theorem 4:51
- Converse of a Statement: Explanation and Example 5:09
- Median, Altitude, and Angle Bisectors of a Triangle 4:50
- Properties of Concurrent Lines in a Triangle 6:17
- Angles and Triangles: Practice Problems 7:43
- Congruency of Right Triangles: Definition of LA and LL Theorems 7:00
- Constructing Triangles: Types of Geometric Construction 5:59
- Constructing the Median of a Triangle 4:47
- The AAS (Angle-Angle-Side) Theorem: Proof and Examples 6:31
- The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples 5:50
- The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples 6:19
- Congruent Sides of a Triangle: Definition & Overview 5:24
- Dihedral Angle: Definition & Calculation
- Double Angle: Properties, Rules, Formula & Examples
- Percent Increase: Definition & Formula
- Sine: Definition & Examples
- Slope-Intercept Form: Definition & Examples 4:59
- What Are Adjacent Angles? - Definition & Examples 3:21
- What is a Central Angle? - Definition, Theorem & Formula 6:04
- Go to NY Regents - Triangles and Congruency: Tutoring Solution

- Foundation Skills Assessment (FSA) Grade 4: Practice & Study Guide
- TECEP Microeconomics: Study Guide & Test Prep
- Alberta Education Diploma - Biology 30: Exam Prep & Study Guide
- Alberta Education Diploma - Mathematics 30-2: Exam Prep & Study Guide
- Alberta Education Diploma - Chemistry 30: Exam Prep & Study Guide
- Understanding Personal Finance
- Translations, Stretches & Reflections of Functions
- Basics of Gerontology
- Unit Conversion & Measurement
- Medical Terms for Radiology, Pharmacology & Oncology
- How to Study Abroad After Graduation
- Is the TABE Test Hard?
- NATA Certification Requirements
- What is on the TABE Test?
- Cyberbullying Organizations
- Study.com and TESU
- Is AP Environmental Science Hard?

- What Is Hypertension (HTN)? - Definition, Symptoms & Causes
- Figurative Language in Beowulf
- Characteristics of Different Ocean Zones
- What Is Task Conflict? - Definition & Explanation
- How to Make a Paper Rocket Ship
- Chief Tecumseh & The War of 1812: Lesson for Kids
- The American Dream in The Grapes of Wrath: Theme & Analysis
- Allusion in The Grapes of Wrath
- Quiz & Worksheet - The Cambodian Genocide
- Quiz & Worksheet - Limiting Adjectives
- Quiz & Worksheet - Features & Limitations of Convenience Sampling
- Quiz & Worksheet - Characteristics of Culture
- Quiz & Worksheet - Elements of Information Systems
- Depression Flashcards
- Money Terms Flashcards

- TASC Writing: Prep and Practice
- Geometry Curriculum Resource & Lesson Plans
- AP English Literature: Exam Prep
- McDougal Littell World History: Online Textbook Help
- McDougal Littell World History: Online Textbook Help
- Solutions: General Chemistry Lesson Plans
- Holt McDougal Earth Science Chapter 4 - Rocks: Mineral Mixtures
- Quiz & Worksheet - Types of Files and File Extensions
- Quiz & Worksheet - Cloud Computing and Databases
- Quiz & Worksheet - MLA Format
- Quiz & Worksheet - President Fillmore and the Compromise of 1850
- Quiz & Worksheet - Ode on a Grecian Urn by Keats

- Boston Massacre: Colonists and the Declaratory and Townshend Acts
- Communication Skills for Customer Service Managers
- Lyndon B. Johnson and the Vietnam War: Learning Objectives & Activities
- Earth Day Poster Ideas
- Pennsylvania Homeschool Laws
- Word Games for Kids
- Praxis Test Dates
- Constitution Lesson Plan
- Storytelling Games for Kids
- How To Create SAT Vocabulary Flashcards
- Typical MBA Curriculum
- Rainy Day Activities for Kids

Browse by subject