Subjects
Biology
Chemistry
AP Chemistry
English
AP English Literature
1
0
Riley de Beer
12/5/2025
Geometry
Straight line equations (Graphs)
100
•
Dec 5, 2025
•
Riley de Beer
@rileydebeer_joyp
The Cartesian plane is where algebra meets visual representation, allowing... Show more
The Cartesian plane has horizontal (x) and vertical (y) axes that intersect at the origin (0,0). Any point can be located using coordinates in the form (x,y).
When drawing straight lines, the table method is your reliable fallback approach. Start by creating a table with three x-values . Then substitute these values into your equation to calculate the corresponding y-values. Once you have three points, plot them on the graph and connect them with a straight line.
For example, to graph y = 2x - 3, substitute x = -1, 0, and 1 to get y-values of -5, -3, and -1. Plot these points and draw your line!
✨ Pro Tip: Always check your work by testing a fourth point that should fall on your line. If it doesn't, you've made a calculation error somewhere.
The gradient-intercept method is a faster way to draw lines when the equation is in the form y = mx + c. First, identify the y-intercept (c) and plot it. Then use the gradient (m) to find a second point by moving from the y-intercept. Connect these points with a ruler.
For equations not already in y = mx + c form, you'll need to rearrange them first. For example, 2y + 3x = 6 becomes y = -3/2x + 3.
When comparing multiple graphs with the same format , notice the patterns: the value of c determines where the line crosses the y-axis, while m controls the steepness and direction. Positive m values make lines go up as x increases, while negative values make them go down.
🔑 Remember: The larger the absolute value of m, the steeper your line will be. A line with m = 5 is steeper than one with m = 2.
The dual intercept method works well for equations in the form ax + by = c. This approach focuses on finding where the line crosses each axis.
To find the y-intercept, set x = 0 and solve for y. Plot this point on the y-axis.
To find the x-intercept, set y = 0 and solve for x. Plot this point on the x-axis.
Once you have both intercepts, simply connect them with a straight line. For example, with 3x - 4y = 12, when x = 0, y = -3, and when y = 0, x = 4. Plot these points and draw your line!
💡 Quick Tip: This method works best when both intercepts are easy to find and plot on your graph paper.
Every straight line can be written as y = mx + c, where c is the y-intercept and m is the gradient or slope (how steep the line is).
The gradient represents the ratio of vertical change to horizontal change as you move along the line. Calculate it using m = / between any two points on the line.
Horizontal lines follow the format y = number , while vertical lines follow x = number (with undefined gradient).
Parallel lines always have equal gradients. If you know two lines are parallel, their m-values must be identical.
Perpendicular lines have gradients that multiply to give -1. To find a perpendicular gradient, flip the fraction upside down and change its sign. For example, if one line has m = 2, a perpendicular line would have m = -1/2.
🎯 Test Prep Alert: Questions about parallel and perpendicular lines appear frequently on math tests, so make sure you understand how to identify and work with their gradients!
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.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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
Riley de Beer
@rileydebeer_joyp
The Cartesian plane is where algebra meets visual representation, allowing you to see equations as lines on a graph. This system lets you plot points, draw lines, and understand the relationships between different equations by visualizing them together.
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The Cartesian plane has horizontal (x) and vertical (y) axes that intersect at the origin (0,0). Any point can be located using coordinates in the form (x,y).
When drawing straight lines, the table method is your reliable fallback approach. Start by creating a table with three x-values . Then substitute these values into your equation to calculate the corresponding y-values. Once you have three points, plot them on the graph and connect them with a straight line.
For example, to graph y = 2x - 3, substitute x = -1, 0, and 1 to get y-values of -5, -3, and -1. Plot these points and draw your line!
✨ Pro Tip: Always check your work by testing a fourth point that should fall on your line. If it doesn't, you've made a calculation error somewhere.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The gradient-intercept method is a faster way to draw lines when the equation is in the form y = mx + c. First, identify the y-intercept (c) and plot it. Then use the gradient (m) to find a second point by moving from the y-intercept. Connect these points with a ruler.
For equations not already in y = mx + c form, you'll need to rearrange them first. For example, 2y + 3x = 6 becomes y = -3/2x + 3.
When comparing multiple graphs with the same format , notice the patterns: the value of c determines where the line crosses the y-axis, while m controls the steepness and direction. Positive m values make lines go up as x increases, while negative values make them go down.
🔑 Remember: The larger the absolute value of m, the steeper your line will be. A line with m = 5 is steeper than one with m = 2.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The dual intercept method works well for equations in the form ax + by = c. This approach focuses on finding where the line crosses each axis.
To find the y-intercept, set x = 0 and solve for y. Plot this point on the y-axis.
To find the x-intercept, set y = 0 and solve for x. Plot this point on the x-axis.
Once you have both intercepts, simply connect them with a straight line. For example, with 3x - 4y = 12, when x = 0, y = -3, and when y = 0, x = 4. Plot these points and draw your line!
💡 Quick Tip: This method works best when both intercepts are easy to find and plot on your graph paper.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Every straight line can be written as y = mx + c, where c is the y-intercept and m is the gradient or slope (how steep the line is).
The gradient represents the ratio of vertical change to horizontal change as you move along the line. Calculate it using m = / between any two points on the line.
Horizontal lines follow the format y = number , while vertical lines follow x = number (with undefined gradient).
Parallel lines always have equal gradients. If you know two lines are parallel, their m-values must be identical.
Perpendicular lines have gradients that multiply to give -1. To find a perpendicular gradient, flip the fraction upside down and change its sign. For example, if one line has m = 2, a perpendicular line would have m = -1/2.
🎯 Test Prep Alert: Questions about parallel and perpendicular lines appear frequently on math tests, so make sure you understand how to identify and work with their gradients!
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.
You can download the app in the Google Play Store and in the Apple App Store.
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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What are some important lines relationships in space? On a plane? And what are some of the angle relationships associated with parallel line relations? And how do we use them in algebraic problem solving?
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GeometryThese are basically all the postulates and theorems for geometry to prove different shapes, typically triangles.
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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
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