Graphs are everywhere in maths and real life - from...
Maths508 views·Updated 23 Jul 2026·2 pagesUnderstanding Graphs in Mathematics
B€LA〄@bxla
1
of 2
Graph Fundamentals and Line Equations
Understanding graphs starts with knowing that they show relationships between two variables plotted on axes. Think of it like a visual way to see how one thing affects another - brilliant for spotting patterns quickly!
The equation of a straight line follows the format y = mx + c, where m is the gradient (how steep the line is) and c is the y-intercept (where the line crosses the y-axis). To find any line's equation, simply work out the gradient first, then spot where it hits the y-axis.
Parallel lines have identical gradients but different y-intercepts, whilst perpendicular lines meet at right angles. When drawing graphs, you'll complete a table of values by substituting x-values into your equation, then plot these coordinate points and join them with a straight line.
Quick Tip: Always double-check your plotted points - one wrong coordinate can throw off your entire line!
2
of 2
Distance Formulas and Real-Life Applications
Finding the midpoint between two points is dead simple - just find the average of the x-coordinates and the average of the y-coordinates. The formula looks scary, but it's basically finding the mean twice!
The distance formula uses Pythagoras' theorem to calculate how far apart two points are. You're creating a right-angled triangle and finding the hypotenuse length - perfect for working out actual distances on coordinate grids.
Distance-time graphs bring maths into the real world by showing journeys. The gradient tells you the speed (steeper = faster), flat sections show stops, and you can read off distances and times directly from the axes. These graphs are brilliant for analysing everything from car journeys to delivery routes.
Remember: On distance-time graphs, a steeper line means higher speed - horizontal lines mean you've stopped completely!
We thought you’d never ask...
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1180,1386,322
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
78913
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,62462
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
115641
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
119743
M
MathsMaths Made Easy: Essential Concepts for Grade 7
Master key mathematical concepts with this comprehensive flashcard set designed specifically for 13-year-old students. Strengthen your understanding and ace your exams!
77922
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
73213
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
112240
MathsGCSE Maths Revision Guide
Comprehensive solutions and explanations for past GCSE Maths Paper 1 questions. Topics include solving quadratics, area calculations, ratios, probability, and more. Ideal for students preparing for their exams, with clear step-by-step methods and key concepts highlighted.
111,42317
Most popular content
9
SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,7982,306
SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,9863,041
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8981,061
SociologyComprehensive Crime & Deviance Overview
Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.
1251,6721,401
C
BiologyCell Biology and Cell structure
cell structures
113,2990
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,177125
SociologySociological Theories Overview
Comprehensive revision of key sociological theories including Functionalism, Marxism, Feminism, and Interpretivism. Explore concepts like value freedom, identity formation, and the critique of social control. Ideal for AQA A-Level Sociology students preparing for exams. This summary covers essential theories and their implications in sociology, providing a clear understanding of each perspective.
1231,494846
T
BiologyThe functions of subcellular structures - B1 Biology
Flashcards on the different functions of subcellular structures: cell membrane, nucleus, mitochondria, ribosomes, cytoplasm, permant vacuole, chloroplasts and cell wall.
112,8215
1
Biology1.cells Gcse biology question cards
combined science higher biology
112,3734
Students love us — and so will you.
4.6/5App Store
4.7/5Google 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 SiOS 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 KlichAndroid 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.
AnnaiOS user
Maths508 views·Updated 23 Jul 2026·2 pagesUnderstanding Graphs in Mathematics
B€LA〄@bxla
Graphs are everywhere in maths and real life - from tracking your phone battery to plotting journeys on maps. This topic covers everything you need to master straight line graphs, from writing equations to interpreting distance-time graphs that show real-world...
1
of 2
Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Graph Fundamentals and Line Equations
Understanding graphs starts with knowing that they show relationships between two variables plotted on axes. Think of it like a visual way to see how one thing affects another - brilliant for spotting patterns quickly!
The equation of a straight line follows the format y = mx + c, where m is the gradient (how steep the line is) and c is the y-intercept (where the line crosses the y-axis). To find any line's equation, simply work out the gradient first, then spot where it hits the y-axis.
Parallel lines have identical gradients but different y-intercepts, whilst perpendicular lines meet at right angles. When drawing graphs, you'll complete a table of values by substituting x-values into your equation, then plot these coordinate points and join them with a straight line.
Quick Tip: Always double-check your plotted points - one wrong coordinate can throw off your entire line!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Distance Formulas and Real-Life Applications
Finding the midpoint between two points is dead simple - just find the average of the x-coordinates and the average of the y-coordinates. The formula looks scary, but it's basically finding the mean twice!
The distance formula uses Pythagoras' theorem to calculate how far apart two points are. You're creating a right-angled triangle and finding the hypotenuse length - perfect for working out actual distances on coordinate grids.
Distance-time graphs bring maths into the real world by showing journeys. The gradient tells you the speed (steeper = faster), flat sections show stops, and you can read off distances and times directly from the axes. These graphs are brilliant for analysing everything from car journeys to delivery routes.
Remember: On distance-time graphs, a steeper line means higher speed - horizontal lines mean you've stopped completely!
We thought you’d never ask...
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1180,1386,322
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
78913
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,62462
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
115641
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
119743
M
MathsMaths Made Easy: Essential Concepts for Grade 7
Master key mathematical concepts with this comprehensive flashcard set designed specifically for 13-year-old students. Strengthen your understanding and ace your exams!
77922
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
73213
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
112240
MathsGCSE Maths Revision Guide
Comprehensive solutions and explanations for past GCSE Maths Paper 1 questions. Topics include solving quadratics, area calculations, ratios, probability, and more. Ideal for students preparing for their exams, with clear step-by-step methods and key concepts highlighted.
111,42317
Most popular content
9SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,7982,306
SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,9863,041
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8981,061
SociologyComprehensive Crime & Deviance Overview
Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.
1251,6721,401
C
BiologyCell Biology and Cell structure
cell structures
113,2990
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,177125
SociologySociological Theories Overview
Comprehensive revision of key sociological theories including Functionalism, Marxism, Feminism, and Interpretivism. Explore concepts like value freedom, identity formation, and the critique of social control. Ideal for AQA A-Level Sociology students preparing for exams. This summary covers essential theories and their implications in sociology, providing a clear understanding of each perspective.
1231,494846
T
BiologyThe functions of subcellular structures - B1 Biology
Flashcards on the different functions of subcellular structures: cell membrane, nucleus, mitochondria, ribosomes, cytoplasm, permant vacuole, chloroplasts and cell wall.
112,8215
1
Biology1.cells Gcse biology question cards
combined science higher biology
112,3734
Students love us — and so will you.
4.6/5App Store
4.7/5Google 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 SiOS 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 KlichAndroid 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.
AnnaiOS user