Year 8 Term 1 Week 9 - Non Linear Graphs
- Sallyann Clark
- 4 days ago
- 4 min read
Week 3 – Non-linear Graphs
Introduction
This week, we move beyond straight lines to explore quadratic graphs, reciprocal graphs, and compare linear with non-linear graphs.
What I should already know
How to plot straight line graphs.
How to substitute values into equations.
How to work with positive and negative numbers.
Real-world application – Why it matters
Non-linear graphs model real-world curves: parabolas for projectiles, reciprocal graphs for inverse relationships like speed and time. They help us understand more complex patterns.
Day 1 – Quadratic Graphs
What am I Learning Today?
I will be learning to plot simple quadratic graphs.
Revision Reminder
Quadratic means the highest power of x is 2, e.g.
Game
Wordwall - Algebra game.
Learn
Watch Fuseschool - Drawing Quadratic Graphs.
Task
Plot:
Glue your graphs into your journal, label them and explain their shapes.
Conclusion
You can now recognise and plot quadratic graphs.
Day 2 – Reciprocal Graphs
What am I Learning Today?
I will be learning to plot graphs of
Revision Reminder
Remember how to substitute positive and negative numbers into an equation to generate a table of values.
Game
Play Mathnook- 4 wheel fracas.
Learn
Watch Fuseschool - Recipricol Graphs.
Watch Fuseschool - Asymptotes
Task
Plot
for x=-5 to 5 (excluding 0).
In your journal:
Glue your graph into your journal, label it and explain its shape. Label the asymptotes and define asymptotes.
Conclusion
You can now plot reciprocal graphs with asymptotes.
Day 3 – Comparing Graphs
What am I Learning Today?
I will be learning to compare linear and non-linear graphs.
Revision Reminder
Linear graphs are straight. Non-linear graphs curve or bend. It is helpful if you know how to describe the shape of graphs and linear relationships.
Watch White Rose Maths - Understand and Describe Linear Correlation.
Game
Play Wordwall - Describing Graphs
Learn
I found it challenging to find a resource for you today, so you have me to explain!
A linear graph is always a straight line. It comes from an equation where the highest power of x is 1, for example:
y = 2x + 1
y = −xy
Linear graphs have:
A constant gradient (the slope never changes).
A straight line that goes on forever in both directions.
A simple rule: “add/subtract the same amount each time.”
A non-linear graph is any graph that is not a straight line. The equation will usually have powers of x greater than 1, or in the denominator, for example:
(a quadratic, U-shaped curve)
(a reciprocal graph with two curves)
Non-linear graphs have:
A changing gradient (the slope gets steeper or shallower).
Curves, bends, or asymptotes (lines they approach but never cross).
Rules where the change is not constant. For example, in a quadratic sequence, the differences between terms change each time.
How to compare them:
Look at the shape: straight = linear, curved = non-linear.
Look at the equation: highest power of x = 1 → linear; higher than 1 or in the denominator → non-linear.
Look at the rate of change: linear graphs increase/decrease steadily; non-linear graphs change more quickly or slowly.
Example:
The graph of y = 2x + 1 is a straight line with constant gradient 2.
The graph of
curves upwards, starting shallow and getting steeper as x grows.
Task
Khan Academy - Algebra 1 Unit 4 Lesson 5 Applying intercepts and Slopes.
In your journal;
make a note of the differences between linear and non-linear graphs.
Conclusion
You can distinguish between straight and curved graphs.
Day 4 – Finding the Equation of a Line Through Two Points
What am I Learning Today?
I will be learning to find the equation of a straight line given two points.
Revision Reminder
Remember how to calculate the gradient of a line between two points:
This is the first step in building the full equation of the line.
Game
Maths 10 - Linear Functions Game.
Learn
Watch Fuseschool - Find the Equation of a Line Through Two Points part 1 & 2.
Task
MEP Year 8 14.5 - The Equation of a Line Given Two Points.
Conclusion
You can now use graphs to estimate solutions.
Day 5 – Project: Designing a Park Map with Graphs
What am I learning today?
I will be learning to use quadratic, reciprocal, and linear equations (found from two points) to design and explain a real-world style map.
Task
Imagine you are designing a mathematical park map.
Quadratic Curve
Use an equation like
to represent a curved path (e.g. a hill or archway). Plot at least 5 points.
Reciprocal Curve
Use y = 1/x to represent another feature (e.g. two curved walkways that never touch the axes).
Straight Line Through Two Points
Choose two points, e.g. (1, 3) and (5, 7). Find the equation of the line that passes through them to represent a footpath.
Label each part of your map with its equation.
Write 2–3 sentences in your journal explaining:
How did you find the equation of your straight line?
How the different types of graphs (linear, quadratic, and reciprocal) give your park different shapes and features.
Conclusion
You have combined linear and non-linear graphs in a creative project, using the method of finding a line through two points and showing how equations can describe real-world features.
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