Equation of a Straight Line
A straight line can be written as y equals mx plus c, where m is the gradient and c is the y-intercept.
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Play with the controls to see the idea in action.
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A straight line can be written as y equals mx plus c, where m is the gradient and c is the y-intercept.
- m is the slope and c is where it crosses the y-axis
- Perpendicular gradients multiply to -1
- Use two points to find the equation
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Equation of a Straight Line?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Equation of a Straight 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 Equation of a Straight Line in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Equation of a Straight Line gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Equation of a Straight Line in detail
The equation of a straight line is commonly written y = mx + c, where m is the gradient and c is the y-intercept, the point where the line crosses the y-axis. So y = 2x + 1 rises 2 for every 1 across and cuts the y-axis at 1.
To find an equation, work out the gradient from two points, then substitute one point to find c. Lines can also be written as ax + by = c and may need rearranging into the standard form. Straight-line equations model constant rates such as taxi fares with a fixed charge plus a cost per kilometre.
How the interactive helps you understand Equation of a Straight 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 Equation of a Straight Line.
Real-life uses and examples
- Explain Equation of a Straight Line to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Equation of a Straight Line in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Equation of a Straight Line by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Equation of a Straight Line without checking why they work.
- Forgetting units, signs or brackets when you apply Equation of a Straight Line.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Equation of a Straight Line
What is Equation of a Straight Line?
A straight line can be written as y equals mx plus c, where m is the gradient and c is the y-intercept.
What are the most important points about Equation of a Straight Line?
The main points are: m is the slope and c is where it crosses the y-axis; Perpendicular gradients multiply to -1; Use two points to find the equation.
Why is Equation of a Straight Line useful?
Understanding Equation of a Straight Line gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Equation of a Straight 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 Equation of a Straight Line?
Related topics in Mathematics include Cubic and Reciprocal Graphs, Distance-Time Graphs, Composite and Inverse Functions.