Calculator
Choose a solving method, enter values, and compute slope, intercepts, standard form, function value, and a plotted graph.
Formula used
The main linear function form is y = mx + b.
- m is the slope, or rate of change.
- b is the y-intercept, where the line crosses the y-axis.
- Function value: f(x) = mx + b
- Two-point slope: m = (y₂ − y₁) / (x₂ − x₁)
- Point-slope relation: y − y₁ = m(x − x₁)
- X-intercept: x = −b / m, when m ≠ 0
This calculator converts each method into slope-intercept form, then computes intercepts, evaluated values, and a graph-friendly point table.
How to use this calculator
- Select a solving mode that matches your data.
- Enter slope and intercept, one point with slope, or two points.
- Type the x-value you want to evaluate.
- Press Calculate Linear Function.
- Review the equation, intercepts, standard form, angle, graph, and generated table.
- Use the CSV button for spreadsheet work.
- Use the PDF button to save a report view.
Example data table
Example line: y = 2x + 3
This sample helps you verify how the calculator builds points from a slope and intercept.
| x | Computed y | Explanation |
|---|---|---|
| -2 | -1 | 2(-2) + 3 = -1 |
| 0 | 3 | The y-intercept is 3 |
| 2 | 7 | 2(2) + 3 = 7 |
| 4 | 11 | 2(4) + 3 = 11 |
Frequently asked questions
1. What is a linear function?
A linear function is a relationship where output changes at a constant rate. Its graph is a straight line, often written as y = mx + b.
2. What does slope mean?
Slope measures how much y changes when x increases by one unit. A positive slope rises, a negative slope falls, and zero slope gives a horizontal line.
3. What is the y-intercept?
The y-intercept is the point where the line crosses the y-axis. In y = mx + b, the intercept is the value b, located at x = 0.
4. Can this calculator work from two points?
Yes. Enter two points, and the calculator first finds slope using the change in y over the change in x. Then it derives the full function.
5. Why is a vertical line rejected?
A vertical line has an undefined slope and cannot be written as y = mx + b. That means it is not a linear function of y versus x.
6. What is the x-intercept?
The x-intercept is where the line crosses the x-axis. At that point, y = 0, so the calculator solves 0 = mx + b to find x.
7. Why does the calculator show a point table?
The table gives sample coordinates from your line. It helps with graphing, checking patterns, exporting data, and confirming calculated results quickly.
8. When should I download CSV or PDF?
Use CSV when you want editable numerical data in spreadsheet software. Use PDF when you want a clean shareable report for printing, homework, or documentation.