Linear Equation Explorer (y = mx + b)
Change slope and intercept or drag two points to see the line, its equation and intercepts.
About the Linear Equation Explorer (y = mx + b)
Free interactive line grapher. Adjust slope and y-intercept or drag two points and see the equation in slope-intercept, point-slope and standard form, plus intercepts and angle. Built for math, the linear equation explorer (y = mx + b) runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Change slope and intercept or drag two points to see the line, its equation and intercepts. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Linear Equation Explorer (y = mx + b)
- Use the controls to change Slope m, y-intercept b. The simulation reacts instantly.
- Pick an option such as Slope & intercept, Two points to switch modes or load an example.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Set the slope to 0 and then negative.
- Use Two points mode and drag the points.
- Find the x-intercept.
- Make two parallel lines.
Key ideas you can learn
- Slope m is rise over run, and b is where the line crosses the y-axis.
- Two points are enough to define a line: m = (y₂ − y₁) / (x₂ − x₁).
- Parallel lines share a slope, and perpendicular slopes multiply to −1.
Where this is used in the real world
Straight-line graphs model speed, cost, temperature conversions and trends in data. Slope and intercept are used everywhere in science and business.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
How do I find the slope from two points?
Subtract the y-values and divide by the difference of the x-values: m = (y₂ − y₁) / (x₂ − x₁).
What does a negative slope mean?
The line goes down as you move right, so y decreases while x increases.
Is the Linear Equation Explorer (y = mx + b) free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Linear Equation Explorer (y = mx + b) work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.