Gradient of a Line
The gradient measures how steep a line is, found as the change in y divided by the change in x.
▶ Interact
Play with the controls to see the idea in action.
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The gradient measures how steep a line is, found as the change in y divided by the change in x.
- Positive gradients slope upward
- Negative gradients slope downward
- Parallel lines have equal gradients
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Gradient of a Line?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Gradient of a Line. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Gradient of a Line in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Gradient of a Line gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Gradient of a Line in detail
The gradient measures how steep a line is: change in y divided by change in x, often written rise over run. A line going up from left to right has a positive gradient, one going down has a negative gradient, a horizontal line has gradient 0 and a vertical line has an undefined gradient.
To find it from two points (x₁, y₁) and (x₂, y₂), calculate (y₂ − y₁)/(x₂ − x₁). Parallel lines have equal gradients, and perpendicular lines have gradients whose product is −1. In real graphs the gradient represents a rate, such as speed on a distance-time graph.
How the interactive helps you understand Gradient of a Line
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Gradient of a Line.
Real-life uses and examples
- Use Gradient of a Line when comparing prices, discounts or recipe quantities in everyday life.
- Explain Gradient of a Line to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Gradient of a Line in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Gradient of a Line.
- Memorising the steps for Gradient of a Line without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Gradient of a Line
What is Gradient of a Line?
The gradient measures how steep a line is, found as the change in y divided by the change in x.
What are the most important points about Gradient of a Line?
The main points are: Positive gradients slope upward; Negative gradients slope downward; Parallel lines have equal gradients.
Why is Gradient of a Line useful?
Understanding Gradient of a Line gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Gradient of a Line?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Gradient of a Line?
Related topics in Mathematics include Quadratic Graphs, Transformations of Graphs, Functions.