Maths · KS3 and GCSE · Interactive lesson
Straight-line graphs: gradient and intercept
Explore y = mx + c. Change the gradient and intercept, read points and connect a straight-line equation to its graph.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Connect a straight line’s steepness and where it crosses the y-axis with its equation.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- x gives a point’s horizontal position (across); y gives its vertical position (up or down).
- The gradient tells you the change in y for 1 step to the right.
- The y-intercept is where the line crosses the y-axis, at x = 0.
Useful starting points
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What do the words mean?
- Coordinates (x, y)
- A point’s horizontal position and vertical position.
- Gradient (m)
- Change in y divided by change in x.
- y-intercept (c)
- The value of y where the line crosses the y-axis, at x = 0.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the gradient the same. Change the intercept. Does the line become steeper or move up and down?
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
Both axes run from −5 to 5, with one unit per square. Purple: your line. Orange: (0, c). Green dashed step: 1 right, then the change in y. The line carries on beyond the grid shown.
More about this diagram
Still picture. Play particle motion in Stage 2.
1 right: y moves 1 up · y-intercept 0
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- Start at (0, 0).
- Move 1 right to x = 1: y moves 1 up.
- The gradient is 1. The second point is (1, 1).
- The orange dot is (0, 0): the y-intercept is 0.
Try on your own
Your turn. No rush.
Question 1
A straight line crosses the y-axis at 2. What is its y-intercept?
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
A good place to pause
This recap is for the activity you just tried. You can return to other activities in this topic later.
Can you read two points and explain how gradient and the y-intercept affect a line?
Try one question and explain your first step. If you need help, use a hint, go back to the idea, or ask Maurice. You choose the pace.
Explain it in your own words and add a small example. This can help you remember and spot what to ask Maurice.
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
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