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235

May 8, 2023

7 pages

Learn How to Find and Graph the Slope Between Two Points

A comprehensive guide to understanding slope and rate of change... Show more

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Practical Application: Thunder and Lightning

This section demonstrates how to graph data and calculate slope using a real-world example involving thunder and lightning distance calculations.

Example: A table showing the relationship between seconds to hear thunder and miles from a lightning strike is used to illustrate slope calculation.

Highlight: The graphing process involves plotting ordered pairs and drawing a right triangle to determine rise and run.

Definition: The slope is calculated by counting the vertical and horizontal changes on the graph, represented as a fraction of rise over run.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Slope Formula Application

This page introduces the formal slope formula method for calculating rate of change.

Definition: The slope formula is expressed as changeinychange in y/changeinxchange in x or y2y1y₂-y₁/x2x1x₂-x₁

Example: Using the points 3,153, 15 and 5,255, 25 to calculate slope in the thunder/lightning scenario.

Highlight: The calculated slope of 5 represents that for every 5 seconds between lightning and thunder, there is 1 mile distance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Plant Growth Analysis

This section applies slope concepts to analyze plant growth over time.

Example: A science fair project tracking plant height over weeks demonstrates practical slope calculation.

Highlight: The slope calculation shows that the plant grows 1.5 cm each week, or alternatively, 3 cm every 2 weeks.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Fruit Snacks Distribution

This page demonstrates slope calculation in a packaging context.

Example: Analysis of fruit snack packs per box shows how slope represents a packaging ratio.

Highlight: The calculated slope of 4 indicates that there are 4 packs for each box.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Financial Application: Savings Account

This section applies slope concepts to financial scenarios.

Example: Renaldo's savings account with weekly $300 deposits illustrates constant rate of change.

Highlight: The slope of 300 represents the weekly increase in account balance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Cell Phone Account Analysis

This final section demonstrates slope application in a practical financial scenario.

Example: Jessica's cell phone account balance increases by 10weeklyfromaninitial10 weekly from an initial 45.

Highlight: The slope of 10 represents the consistent weekly increase in account balance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

Introduction to Slope

This page introduces the fundamental concept of slope in mathematics. The content focuses on understanding slope as a measure of steepness and rate of change between points on a line.

Definition: Slope is the rate of change between any two points on a line, representing the steepness of that line.

Vocabulary:

  • Rise: The vertical change between two points
  • Run: The horizontal change between two points

Highlight: Slope can be visualized and calculated using the relationship between vertical change riserise and horizontal change runrun.



Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

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

iOS user

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

iOS user

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

iOS user

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

iOS user

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

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

iOS user

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

iOS user

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

iOS user

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

iOS user

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

 

Arithmetic

235

May 8, 2023

7 pages

Learn How to Find and Graph the Slope Between Two Points

A comprehensive guide to understanding slope and rate of change in mathematics, focusing on calculating slope between two points on a line and graphing and interpreting slope from data.

  • Introduces the fundamental concept of slope as the rate of... Show more

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Practical Application: Thunder and Lightning

This section demonstrates how to graph data and calculate slope using a real-world example involving thunder and lightning distance calculations.

Example: A table showing the relationship between seconds to hear thunder and miles from a lightning strike is used to illustrate slope calculation.

Highlight: The graphing process involves plotting ordered pairs and drawing a right triangle to determine rise and run.

Definition: The slope is calculated by counting the vertical and horizontal changes on the graph, represented as a fraction of rise over run.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Slope Formula Application

This page introduces the formal slope formula method for calculating rate of change.

Definition: The slope formula is expressed as changeinychange in y/changeinxchange in x or y2y1y₂-y₁/x2x1x₂-x₁

Example: Using the points 3,153, 15 and 5,255, 25 to calculate slope in the thunder/lightning scenario.

Highlight: The calculated slope of 5 represents that for every 5 seconds between lightning and thunder, there is 1 mile distance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Plant Growth Analysis

This section applies slope concepts to analyze plant growth over time.

Example: A science fair project tracking plant height over weeks demonstrates practical slope calculation.

Highlight: The slope calculation shows that the plant grows 1.5 cm each week, or alternatively, 3 cm every 2 weeks.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Fruit Snacks Distribution

This page demonstrates slope calculation in a packaging context.

Example: Analysis of fruit snack packs per box shows how slope represents a packaging ratio.

Highlight: The calculated slope of 4 indicates that there are 4 packs for each box.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Financial Application: Savings Account

This section applies slope concepts to financial scenarios.

Example: Renaldo's savings account with weekly $300 deposits illustrates constant rate of change.

Highlight: The slope of 300 represents the weekly increase in account balance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Cell Phone Account Analysis

This final section demonstrates slope application in a practical financial scenario.

Example: Jessica's cell phone account balance increases by 10weeklyfromaninitial10 weekly from an initial 45.

Highlight: The slope of 10 represents the consistent weekly increase in account balance.

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope

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

Introduction to Slope

This page introduces the fundamental concept of slope in mathematics. The content focuses on understanding slope as a measure of steepness and rate of change between points on a line.

Definition: Slope is the rate of change between any two points on a line, representing the steepness of that line.

Vocabulary:

  • Rise: The vertical change between two points
  • Run: The horizontal change between two points

Highlight: Slope can be visualized and calculated using the relationship between vertical change riserise and horizontal change runrun.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

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

iOS user

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

iOS user

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

iOS user

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

iOS user

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

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

iOS user

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

iOS user

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

iOS user

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

iOS user

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