Explore the Linear Equation Explorer
Change slope and intercept or drag two points to see the line, its equation and intercepts. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Linear Equation Explorer with sample data entered and the result showing.
What is the Linear Equation Explorer?
Change slope and intercept or drag two points to see the line, its equation and intercepts. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Straight-line graphs model speed, cost, temperature conversions and trends in data. Slope and intercept are used everywhere in science and business.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
Set the slope to 0 and then negative.
Use Two points mode and drag the points.
Find the x-intercept.
Used for
Pick one to see how it fits.
Math learners
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
Try it freeTeachers
For teachers: project the Linear Equation Explorer (y = mx + b) on the board, let students predict the result, then run it together and test this: Use Two points mode and drag the points. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Linear Equation Explorer (y = mx + b) is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Linear Equation Explorer (y = mx + b) work on a phone or tablet?
Yes. The Linear Equation Explorer (y = mx + b) takes touch input as well as mouse input, so you can use its 2 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Linear Equation Explorer?
1. In the Linear Equation Explorer (y = mx + b), use the controls to change Slope m, y-intercept b. The simulation reacts instantly. 2. In the Linear Equation Explorer (y = mx + b), pick an option such as Slope & intercept, Two points to switch modes or load an example. 3. In the Linear Equation Explorer (y = mx + b), press "Reset line" to start, reset or change what is happening. 4. Start with this experiment: Set the slope to 0 and then negative. Drag any glowing handle, object or slider with your mouse or finger and the Linear Equation Explorer (y = mx + b) responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: Slope m is rise over run, and b is where the line crosses the y-axis.
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Try the Linear Equation Explorer now
Change slope and intercept or drag two points to see the line, its equation and. Free to use.
Try it free