Linear Equation Explorer (y = mx + b)
Change slope and intercept or drag two points to see the line, its equation and intercepts.
What the Linear Equation Explorer (y = mx + b) shows
Change slope and intercept or drag two points to see the line, its equation and intercepts. Free, no signup, runs in your browser. 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 and equation.
How to use the Linear Equation Explorer (y = mx + b)
In the Linear Equation Explorer (y = mx + b), use the controls to change Slope m, y-intercept b. The simulation reacts instantly.
In the Linear Equation Explorer (y = mx + b), pick an option such as Slope & intercept, Two points to switch modes or load an example.
In the Linear Equation Explorer (y = mx + b), press "Reset line" to start, reset or change what is happening.
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.
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.
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.
The science behind it
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.
A worked example with real numbers
m = 6 / 3 = 2 b = 3 - 2 x 1 = 1 y = 2x + 1; x-intercept -0.5
Tips and common mistakes
Tips
- Make the slope negative.
- Find intercepts.
Common mistakes
- Swapping x and y.
- Dividing in the wrong order.
Where this is used
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. A good first experiment in the Linear Equation Explorer (y = mx + b): Set the slope to 0 and then negative. The key relation to keep an eye on: y = m x + b; m = (y2 - y1) / (x2 - x1).
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.
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. 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.
