The Graphing Lines simulation from PhET lets you explore how linear equations, slope and graphs of lines are connected. You can drag points and lines, see the equation change, and test yourself in the line game. It is free, runs in any browser on a phone, tablet or laptop, and it is a great fit for the coordinate geometry and linear equations lessons in Tamil Nadu State Board (Samacheer Kalvi) Maths.
What is the Graphing Lines simulation?
This interactive simulation lets you explore the world of lines. You can see how the slope and the intercept of a line show up in its equation and on its graph, and you can test what you have learned in the line game. Because it runs on HTML5, there is nothing to install, and it works on phones, tablets, Chromebooks and computers.
Middle school to high school
Slope, intercept and linear equations
Phone, tablet, Chromebook, PC
English
PhET’s learning goals are to explain how the slope of a graphed line is computed, to graph a line from an equation in slope-intercept or point-slope form, to write an equation from a graphed line, and to predict how changing the variables in a linear equation changes the graph.
Launch the Graphing Lines simulation online
Tap or click inside the player and start exploring. Use the full-screen button in the player for a bigger view.
Credit: University of Colorado Boulder
How to use the Graphing Lines simulation, step by step
- Predict first. Before you change anything, say whether you expect the line to go up or down.
- Explore slope. Look at how the rise and the run of the line give its slope.
- Explore the equation. Change the slope and the intercept in the equation and watch the line move.
- Try both forms. Work with the slope-intercept form and the point-slope form of the same line.
- Play the line game. Graph lines from equations and write equations from graphs to test yourself.
Tip for students: always find the slope first. It tells you how steep the line is and which way it leans.
The idea behind the simulation: y = mx + b
y = m x + b
Here m is the slope and b is the y-intercept, the point where the line crosses the y-axis. The slope is rise over run: m = (y₂ − y₁) ÷ (x₂ − x₁). The point-slope form is y − y₁ = m(x − x₁), which you can use when you know the slope and one point on the line.
Worked example: A line goes through (1, 3) and (3, 7). The slope is (7 − 3) ÷ (3 − 1) = 4 ÷ 2 = 2. Putting the point (1, 3) in y = 2x + b gives 3 = 2 + b, so b = 1. The equation is y = 2x + 1. In point-slope form it is y − 3 = 2(x − 1).
Graphing lines key terms explained
These are the words you will meet while using the Graphing Lines simulation, with simple meanings.
Slope
How steep a line is. It equals rise divided by run.
Rise
The change in y between two points on the line.
Run
The change in x between two points on the line.
Y-intercept
The point where the line crosses the y-axis, where x = 0.
Linear equation
An equation whose graph is a straight line.
Slope-intercept form
The form y = mx + b, which shows the slope and the y-intercept.
Point-slope form
The form y − y₁ = m(x − x₁), built from a point and the slope.
Coordinates
A pair of numbers (x, y) that gives the position of a point on the graph.
Common mistakes: Subtracting the coordinates in a different order on the top and bottom of the slope, mixing up rise and run, and reading the y-intercept from the x-axis instead of the y-axis.
Try the line calculator (practice what you explore)
Enter two points on a line to find its slope, y-intercept and equation. Then tap a “what if” button.
What happens when you change a variable
| Change | Effect on the line |
|---|---|
| Positive slope (m > 0) | The line goes up from left to right |
| Negative slope (m < 0) | The line goes down from left to right |
| Larger slope (ignoring sign) | The line gets steeper |
| Slope of 0 | The line is horizontal |
| Change b | The line moves up or down, with the same steepness |
Classroom activities for teachers
The Graphing Lines simulation fits a single 40-minute period.
- Predict and test (10 min): students sketch a line from an equation, then check it in the simulation.
- Slope hunt (10 min): students find the rise and run of several lines and write down each slope.
- Write the equation (10 min): students read a graph and write its equation in both forms.
- Exit ticket (10 min): students explain in two sentences what the numbers m and b tell you about a line.
Looking for the matching chapters? Browse the Maths books on TN SchoolBooks and download the Samacheer Kalvi PDFs, then use this simulation to make the coordinate geometry lessons visual. More free simulations and textbook PDFs are on the home page.
Quick quiz: test your understanding of lines
Score: 0 / 5
Graphing Lines simulation: frequently asked questions
Is the Graphing Lines simulation free?
Yes. PhET simulations are free to run online in a browser. Check PhET’s licensing page for reuse terms.
Does it work on a mobile phone?
Yes. It is built with HTML5 and works on phones, tablets and Chromebooks. Use landscape mode or the player’s full-screen button for a bigger view.
How do you find the slope of a line?
Pick two points on the line and divide the change in y by the change in x. That is rise over run, m = (y₂ − y₁) ÷ (x₂ − x₁).
What is the difference between slope-intercept and point-slope form?
Slope-intercept form, y = mx + b, uses the slope and the y-intercept. Point-slope form, y − y₁ = m(x − x₁), uses the slope and any one point on the line. Both describe the same line.
The Graphing Lines simulation turns equations into pictures you can drag, test and see. Explore it, take the quiz above, and keep experimenting until graphing a line feels easy.