Linear function - Definition and Overview

A linear function is a mathematical function term of the form:

f(x) = m x + c

where c is a constant.

This function can also be written

y = m x + c

and plotted on an x,y graph. It forms a straight line, as the name implies.

m is often called the slope or gradient; c the y-intercept, which gives the point of intersection between the graph of the function and the y-axis.

Examples:

• f(x)= 2x + 1

(here m=2, c=1)

• f(x) = x

(m=1, c=0)

• f(x)= 9 x - 2
• f(x)= -3 x + 4

On a line graph, changing m makes the line steeper or shallower, and changing c moves the line up or down.

As mentioned, the line crosses the y-axis at the co-ordinate (0,c). It crosses the x-axis at (-c / m) (solving for 0 = m x + c we get x = -c / m).