The Cartesian plane might seem complicated, but it's actually just... Show more
SociologySign 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
2
0
megan-edith
03/12/2025
Maths
Working in the Cartesian Plane
89
•
3 Dec 2025
•
Mastering Graphs in the Cartesian Plane
megan-edith
@meganedith
1 / 4
Working in the Cartesian Plane
Ever wondered why some lines go straight across or straight up on a graph? Horizontal lines run parallel to the x-axis and have equations like y = -1, which means every single point on that line has the same y-coordinate. It's like drawing a flat line across the page.
Vertical lines work the opposite way - they're parallel to the y-axis with equations like x = 3. Every point on a vertical line shares the same x-coordinate, creating a line that goes straight up and down.
The y = x line is special because it creates a perfect 45° angle when your graph scales are equal. At any point on this line, both coordinates match - like (2,2) or (-6,-6). Think of it as the line where x and y are best friends who always have the same value.
Quick Tip: Remember that the scale on your axes matters! If your x and y scales are different, your y = x line won't look like a perfect 45° angle.
Lines of the Form y = kx
The equation y = kx is where things get interesting - it shows how one variable depends on another. When you see y = 2x, you're basically saying "whatever x is, multiply it by 2 to get y." So if x = 3, then y = 6.
The value of k determines the steepness of your line. A bigger k value creates a steeper line that shoots up quickly, while a smaller k value gives you a gentler slope that hugs closer to the x-axis.
Direct proportion happens when two variables increase at exactly the same rate. Your graph must be a straight line passing through the origin for this to work - if it's curved or wobbly, the variables aren't proportional.
Real-World Connection: Think about hourly wages - if you earn £10 per hour, your total pay (y) equals £10 times hours worked (x). That's y = 10x in action!
Lines in the Form y = x + a and y = mx + c
Lines like y = x + 6 and y = x - 4 are just the basic y = x line that's been shifted up or down the graph. They're all parallel because they have the same gradient - they just start from different positions.
The "a" value shows translation - how far up or down the line has moved. If it's y = x + 5, you've moved the y = x line up by 5 places. If it's y = x - 2, you've dropped it down by 2 places.
For y = mx + c equations, create a table with x-values, multiply each by m, then add c. Each pair gives you coordinates to plot. More points mean more accuracy, so don't be lazy - plot at least three points and check they form a straight line.
Exam Tip: Always join your plotted points with a straight line using a ruler. Wobbly freehand lines will cost you marks, even if your calculations are spot-on!
Lines with Negative Gradients
When your line equation has a negative x value , you get a negative gradient that slopes downwards from left to right. Instead of climbing up the graph, these lines take a downward path.
Negative gradient lines always follow the same pattern - they start high on the left and finish low on the right. The steeper the negative number, the more dramatic the downward slope becomes.
Memory Trick: Think "negative = downhill" - negative gradients always slide downwards as you move from left to right across the graph.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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.
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Mastering Graphs in the Cartesian Plane
megan-edith
@meganedith
The Cartesian plane might seem complicated, but it's actually just a fancy way of plotting points and drawing lines on a graph. Once you understand how horizontal and vertical lines work, along with some basic line equations, you'll be graphing... Show more
Working in the Cartesian Plane
Ever wondered why some lines go straight across or straight up on a graph? Horizontal lines run parallel to the x-axis and have equations like y = -1, which means every single point on that line has the same y-coordinate. It's like drawing a flat line across the page.
Vertical lines work the opposite way - they're parallel to the y-axis with equations like x = 3. Every point on a vertical line shares the same x-coordinate, creating a line that goes straight up and down.
The y = x line is special because it creates a perfect 45° angle when your graph scales are equal. At any point on this line, both coordinates match - like (2,2) or (-6,-6). Think of it as the line where x and y are best friends who always have the same value.
Quick Tip: Remember that the scale on your axes matters! If your x and y scales are different, your y = x line won't look like a perfect 45° angle.
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
Lines of the Form y = kx
The equation y = kx is where things get interesting - it shows how one variable depends on another. When you see y = 2x, you're basically saying "whatever x is, multiply it by 2 to get y." So if x = 3, then y = 6.
The value of k determines the steepness of your line. A bigger k value creates a steeper line that shoots up quickly, while a smaller k value gives you a gentler slope that hugs closer to the x-axis.
Direct proportion happens when two variables increase at exactly the same rate. Your graph must be a straight line passing through the origin for this to work - if it's curved or wobbly, the variables aren't proportional.
Real-World Connection: Think about hourly wages - if you earn £10 per hour, your total pay (y) equals £10 times hours worked (x). That's y = 10x in action!
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
Lines in the Form y = x + a and y = mx + c
Lines like y = x + 6 and y = x - 4 are just the basic y = x line that's been shifted up or down the graph. They're all parallel because they have the same gradient - they just start from different positions.
The "a" value shows translation - how far up or down the line has moved. If it's y = x + 5, you've moved the y = x line up by 5 places. If it's y = x - 2, you've dropped it down by 2 places.
For y = mx + c equations, create a table with x-values, multiply each by m, then add c. Each pair gives you coordinates to plot. More points mean more accuracy, so don't be lazy - plot at least three points and check they form a straight line.
Exam Tip: Always join your plotted points with a straight line using a ruler. Wobbly freehand lines will cost you marks, even if your calculations are spot-on!
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
Lines with Negative Gradients
When your line equation has a negative x value , you get a negative gradient that slopes downwards from left to right. Instead of climbing up the graph, these lines take a downward path.
Negative gradient lines always follow the same pattern - they start high on the left and finish low on the right. The steeper the negative number, the more dramatic the downward slope becomes.
Memory Trick: Think "negative = downhill" - negative gradients always slide downwards as you move from left to right across the graph.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Most popular content in Maths
Most popular content
English - inspector calls quotes and analysis
Quotes from every main character
English Literature10
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user