An affine function has the form f(x) = ax + b and its graph is a straight line. Here, linear function is used in this common calculator sense; strictly linear maps have b = 0.
a is the slope, b is the y-intercept and x is the real independent variable. A first-degree function has a ≠ 0.
For a ≠ 0, the unique root is −b/a. If a = 0 and b ≠ 0, there are no roots. If both are zero, every real number is a root.
Enter a and b, then calculate. Editing a field clears the old result so the steps never describe different coefficients.
For f(x) = 2x − 4, the slope is positive. The line crosses the y-axis at (0, −4) and the x-axis at (2, 0).
The slope measures the change in f(x) for a one-unit increase in x. A zero slope gives a horizontal line. Displayed coordinates are approximations, not exact geometric measurements.
The root, intersection or an intercept may lie outside the graph window. For coordinates beyond 10⁶, only the window [−10, 10] is shown; the exact result remains valid.
Use affine functions for fixed fees plus unit costs, constant-speed motion and simple linear models. These models do not describe every real-world relationship.