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Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

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Maithy Smith

5/24/2023

Algebra 1

Slopes

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Algebra 1

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Slope

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Slope

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

This lesson covers key concepts in linear algebra, focusing on slope calculations and equation forms. Students will learn how to find slope using two points, understanding point-slope form equations, and converting point-slope form to slope-intercept form. The material progresses from basic slope calculations to more complex equation manipulations, providing a solid foundation for linear algebra concepts.

Key points:

  • Slope calculation using the "rise over run" formula
  • Finding slope from two given points
  • Using point-slope form to create linear equations
  • Converting between point-slope and slope-intercept forms
  • Practical applications of linear equations
...

5/24/2023

156

Rate of Change OR Slope Slope is the ratio horizontal rise run Rate of of change "rise over run" M= Example 2: Example 3: Finding Slope from

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Point-Slope Form of an Equation

This page delves into the point-slope form of linear equations, providing a detailed explanation of its structure and application.

Definition: The point-slope form of a linear equation is y - y₁ = mx−x1x - x₁, where x1,y1x₁, y₁ is a point on the line and m is the slope.

The document outlines two scenarios for using point-slope form:

  1. When given a point x1,y1x₁, y₁ and a slope mm
  2. When given two points: x1,y1x₁, y₁ and x2,y2x₂, y₂

Example: For the point 4,14,1 and slope 2, the point-slope form equation is y - 1 = 2x−4x - 4

The page provides a step-by-step process for creating and solving point-slope form equations:

  1. Label the ordered pairss
  2. Identify or calculate the slope
  3. Substitute values into the point-slope form
  4. Convert to slope-intercept form y=mx+by = mx + b

Highlight: Converting point-slope form to slope-intercept form is an essential skill for graphing linear equations.

The document includes two detailed examples, demonstrating how to work with different sets of points and slopes to create and manipulate point-slope form equations.

Rate of Change OR Slope Slope is the ratio horizontal rise run Rate of of change "rise over run" M= Example 2: Example 3: Finding Slope from

View

Practice Problems and Notes

This page offers a series of practice problems to reinforce the concepts of slope calculation and point-slope form equations.

The problems cover various scenarios:

  1. Given a point and slope, write the equation in point-slope form and convert to slope-intercept form
  2. Given two points, find the slope and write the equation in both point-slope and slope-intercept forms
  3. Apply the concepts to a real-world situation involving temperature change over time

Example: For the point 0,−90, -9 and slope 4, the solution progresses from y + 9 = 4x−0x - 0 to y = 4x + 9

The page provides step-by-step solutions for each problem, demonstrating the process of: • Identifying given information • Calculating slope when necessary • Writing equations in point-slope form • Converting equations to slope-intercept form

Highlight: Practice problems help solidify understanding of how to find slope using two points and how to apply this knowledge to create and manipulate linear equations.

The final problem presents a real-world application, asking students to model the temperature change in a pond over time using a linear equation. This demonstrates the practical utility of understanding slope and linear equations in scientific contexts.

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Subjects

Algebra 1

Slope

Slope

 

Algebra 1

•

156

•

May 24, 2023

•

3 pages

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

user profile picture

Maithy Smith

@maithysmith

This lesson covers key concepts in linear algebra, focusing on slope calculations and equation forms. Students will learn how to find slope using two points, understanding point-slope form equations, and converting point-slope form to slope-intercept form. The... Show more

Rate of Change OR Slope Slope is the ratio horizontal rise run Rate of of change "rise over run" M= Example 2: Example 3: Finding Slope from

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Point-Slope Form of an Equation

This page delves into the point-slope form of linear equations, providing a detailed explanation of its structure and application.

Definition: The point-slope form of a linear equation is y - y₁ = mx−x1x - x₁, where x1,y1x₁, y₁ is a point on the line and m is the slope.

The document outlines two scenarios for using point-slope form:

  1. When given a point x1,y1x₁, y₁ and a slope mm
  2. When given two points: x1,y1x₁, y₁ and x2,y2x₂, y₂

Example: For the point 4,14,1 and slope 2, the point-slope form equation is y - 1 = 2x−4x - 4

The page provides a step-by-step process for creating and solving point-slope form equations:

  1. Label the ordered pairss
  2. Identify or calculate the slope
  3. Substitute values into the point-slope form
  4. Convert to slope-intercept form y=mx+by = mx + b

Highlight: Converting point-slope form to slope-intercept form is an essential skill for graphing linear equations.

The document includes two detailed examples, demonstrating how to work with different sets of points and slopes to create and manipulate point-slope form equations.

Rate of Change OR Slope Slope is the ratio horizontal rise run Rate of of change "rise over run" M= Example 2: Example 3: Finding Slope from

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Practice Problems and Notes

This page offers a series of practice problems to reinforce the concepts of slope calculation and point-slope form equations.

The problems cover various scenarios:

  1. Given a point and slope, write the equation in point-slope form and convert to slope-intercept form
  2. Given two points, find the slope and write the equation in both point-slope and slope-intercept forms
  3. Apply the concepts to a real-world situation involving temperature change over time

Example: For the point 0,−90, -9 and slope 4, the solution progresses from y + 9 = 4x−0x - 0 to y = 4x + 9

The page provides step-by-step solutions for each problem, demonstrating the process of: • Identifying given information • Calculating slope when necessary • Writing equations in point-slope form • Converting equations to slope-intercept form

Highlight: Practice problems help solidify understanding of how to find slope using two points and how to apply this knowledge to create and manipulate linear equations.

The final problem presents a real-world application, asking students to model the temperature change in a pond over time using a linear equation. This demonstrates the practical utility of understanding slope and linear equations in scientific contexts.

Rate of Change OR Slope Slope is the ratio horizontal rise run Rate of of change "rise over run" M= Example 2: Example 3: Finding Slope from

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Rate of Change or Slope

This page introduces the concept of slope as a rate of change in mathematics. It explains various ways to express and calculate slope, focusing on the "rise over run" method.

Definition: Slope is the ratio of a line's vertical change compared to its horizontal change.

The page presents multiple representations of slope: • As a ratio of rise to run • As "change in y over change in x" • Using the mathematical formula m = Δy / Δx

Vocabulary: Rise refers to the vertical change, while run refers to the horizontal change.

The document then provides a step-by-step guide for finding slope using two points:

  1. Label the first ordered pair as x1,y1x₁, y₁
  2. Label the second ordered pair as x2,y2x₂, y₂
  3. Substitute values into the slope formula and solve

Example: For points 4,44,4 and 0,10,1, the slope is calculated as m = 1−41-4 / 0−40-4 = -3/4

The page concludes with two more examples, demonstrating how to calculate slope for different sets of points, including cases resulting in negative slopes.

Highlight: Understanding how to calculate slope is crucial for analyzing linear relationships and graphing lines.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user