Linear function
Linear function - theory
A linear function describes a relationship where the change is constant and predictable. Its graph is always a straight line, so it is useful for quick calculations and interpretation.
Check your knowledge
A short quiz will help you quickly spot which concepts are worth reviewing.
What is a linear function?
A linear function is a function that can be written as y = ax + b. For every x, you substitute a number into the formula and get exactly one value of y.
The key idea: when x increases by the same amount, y also changes by the same amount each time. That is why the points of the function lie on one straight line.
slope
rate of change of y
starting point
where the line crosses the Y-axis
formula
y = ax + b
Example: y = 2x + 2
x = -1
y = 2 · (-1) + 2 = 0
x = 0
y = 2 · 0 + 2 = 2
This is point B = (0, 2), the Y-axis intercept.
x = 1
y = 2 · 1 + 2 = 4
What should you remember?
The sign of coefficient a immediately tells you how the graph behaves. It is a quick way to check whether the result makes sense.
a > 0
the function is increasing
a = 0
the function is constant
a < 0
the function is decreasing
Next step
Once you know the general idea, go to the detailed formula explanation or return to the calculator and try a few examples of your own.