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Dec 11, 2025
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Complete Math Study Guide: Linear Equations, Standard Form, Proportional Relationships, and Dimensional Analysis
sunvtea
@sanvitia
1 / 5
Linear Equations Study Guide Overview
When working with linear equations, you'll need to master three main forms: slope-intercept , standard form , and point-slope . Each form is useful in different situations depending on what information you have available.
You'll learn to find the slope and y-intercept from various sources - whether you're looking at a graph, reading data from a table, analyzing a word problem, or working with an equation. These skills are essential for understanding how lines behave.
💡 Study Tip: Create flashcards for each form of linear equation with examples of when to use each one. This will help you quickly identify which approach to use on a test!
The guide also covers domain and range for both continuous and discrete graphs, identifying proportional relationships, and using dimensional analysis to convert units - all practical skills you'll use throughout your math journey.
Forms of Linear Equations
The slope-intercept form is probably the most commonly used form. In this equation, y is your dependent variable (the output), m represents the slope (how steep the line is), x is the independent variable (the input), and b is the y-intercept .
When you're given a slope and y-intercept, just plug them directly into y=mx+b. If you have a slope and one point on the line, substitute the point's coordinates for x and y, then solve for b to find the y-intercept.
If you only have two points on a line, first calculate the slope using the formula m = / (the change in y divided by the change in x). Then use one of your points and the slope you just found to determine the y-intercept.
🔑 Key Concept: Remember that the slope tells you how the line behaves (rising, falling, steep, or gradual), while the y-intercept shows where the line starts on the y-axis when x=0.
Identifying the y-intercept
You can find the y-intercept in several ways depending on what information you have. On a graph, look for where the line crosses the y-axis - this point always has an x-coordinate of 0, so it appears as (0, b) where b is your y-intercept.
In a table of values, look for the row where x=0. The corresponding y-value is your y-intercept. For example, if your table shows that when x=0, y=3, then your y-intercept is (0,3).
When working with word problems, you'll need to use the given information to either write an equation or calculate the y-intercept directly. For equations already in slope-intercept form , the y-intercept is simply the value of b.
🎯 Practice This: Find a linear equation in your textbook and identify its y-intercept using three different methods. This helps reinforce that all methods lead to the same answer!
Domain & Range and Proportional Relationships
Continuous graphs show unbroken lines where you can trace the line without lifting your pencil. For these graphs, the domain and range usually include all possible x and y values unless there are specific restrictions.
Discrete graphs show individual points that aren't connected. These represent situations where only specific values make sense, like the number of people (which can't be fractional) or specific data points from an experiment.
Proportional relationships are special linear relationships where the ratio between x and y values remains constant, and the line passes through the origin (0,0). You can identify these by checking if y/x gives the same value for all data points, or by confirming that y=mx .
🧠 Remember: In a proportional relationship, if you double the x value, the y value doubles too. If you triple x, y triples. This consistent ratio is the defining characteristic!
Dimensional Analysis
Dimensional analysis helps you convert between different units of measurement using a systematic approach. Think of it as a puzzle where you're trying to cancel out unwanted units to get the units you need.
Start by listing all your given measurements and the units you want in your final answer. Then set up a fraction chain where units in the numerator cancel with the same units in the denominator, leaving only your desired unit.
Multiply all the numerical values in your fraction chain to get your final answer. The beauty of dimensional analysis is that it helps you track units throughout your calculation, making it less likely you'll make a mistake.
🚀 Real-World Connection: Dimensional analysis is used constantly in science classes, cooking (converting recipe amounts), shopping (finding the best price per unit), and even space missions! NASA once lost a $125 million Mars orbiter because of a unit conversion error.
We thought you’d never ask...
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Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
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Most popular content: Slope-intercept Form
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4.8/5
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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
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
Complete Math Study Guide: Linear Equations, Standard Form, Proportional Relationships, and Dimensional Analysis
sunvtea
@sanvitia
Linear equations are the foundation of algebra and help us model real-world situations. This guide covers different forms of linear equations, how to identify key components like slope and y-intercept, understand domain and range, recognize proportional relationships, and perform dimensional... Show more
Linear Equations Study Guide Overview
When working with linear equations, you'll need to master three main forms: slope-intercept , standard form , and point-slope . Each form is useful in different situations depending on what information you have available.
You'll learn to find the slope and y-intercept from various sources - whether you're looking at a graph, reading data from a table, analyzing a word problem, or working with an equation. These skills are essential for understanding how lines behave.
💡 Study Tip: Create flashcards for each form of linear equation with examples of when to use each one. This will help you quickly identify which approach to use on a test!
The guide also covers domain and range for both continuous and discrete graphs, identifying proportional relationships, and using dimensional analysis to convert units - all practical skills you'll use throughout your math journey.
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
Forms of Linear Equations
The slope-intercept form is probably the most commonly used form. In this equation, y is your dependent variable (the output), m represents the slope (how steep the line is), x is the independent variable (the input), and b is the y-intercept .
When you're given a slope and y-intercept, just plug them directly into y=mx+b. If you have a slope and one point on the line, substitute the point's coordinates for x and y, then solve for b to find the y-intercept.
If you only have two points on a line, first calculate the slope using the formula m = / (the change in y divided by the change in x). Then use one of your points and the slope you just found to determine the y-intercept.
🔑 Key Concept: Remember that the slope tells you how the line behaves (rising, falling, steep, or gradual), while the y-intercept shows where the line starts on the y-axis when x=0.
Sign up to see the contentIt's free!
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Identifying the y-intercept
You can find the y-intercept in several ways depending on what information you have. On a graph, look for where the line crosses the y-axis - this point always has an x-coordinate of 0, so it appears as (0, b) where b is your y-intercept.
In a table of values, look for the row where x=0. The corresponding y-value is your y-intercept. For example, if your table shows that when x=0, y=3, then your y-intercept is (0,3).
When working with word problems, you'll need to use the given information to either write an equation or calculate the y-intercept directly. For equations already in slope-intercept form , the y-intercept is simply the value of b.
🎯 Practice This: Find a linear equation in your textbook and identify its y-intercept using three different methods. This helps reinforce that all methods lead to the same answer!
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
Domain & Range and Proportional Relationships
Continuous graphs show unbroken lines where you can trace the line without lifting your pencil. For these graphs, the domain and range usually include all possible x and y values unless there are specific restrictions.
Discrete graphs show individual points that aren't connected. These represent situations where only specific values make sense, like the number of people (which can't be fractional) or specific data points from an experiment.
Proportional relationships are special linear relationships where the ratio between x and y values remains constant, and the line passes through the origin (0,0). You can identify these by checking if y/x gives the same value for all data points, or by confirming that y=mx .
🧠 Remember: In a proportional relationship, if you double the x value, the y value doubles too. If you triple x, y triples. This consistent ratio is the defining characteristic!
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
Dimensional Analysis
Dimensional analysis helps you convert between different units of measurement using a systematic approach. Think of it as a puzzle where you're trying to cancel out unwanted units to get the units you need.
Start by listing all your given measurements and the units you want in your final answer. Then set up a fraction chain where units in the numerator cancel with the same units in the denominator, leaving only your desired unit.
Multiply all the numerical values in your fraction chain to get your final answer. The beauty of dimensional analysis is that it helps you track units throughout your calculation, making it less likely you'll make a mistake.
🚀 Real-World Connection: Dimensional analysis is used constantly in science classes, cooking (converting recipe amounts), shopping (finding the best price per unit), and even space missions! NASA once lost a $125 million Mars orbiter because of a unit conversion error.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Algebra 1Most popular content: Slope-intercept Form
Most popular content in Algebra 1
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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