Understanding Linear Functions: Definition, Slope & Intercept

A linear function relates a dependent variable (y) and an independent variable (x) with a straight line equation or formula. The dependent variable is a function of the independent variable.

Mathematically, it is represented as:

$$f(x) = mx + b,$$

where \(m\) is the slope of the line and \(b\) is the y-intercept.

Characteristics of a linear function:

The line is straight.

The rate of change (slope) is constant for a linear function.

For every change in the independent variable \(x\) by one unit, the dependent variable \(y \) changes by \( m \) units.