# Linear Term: Definition, Examples

A linear term has a degree of 1. For example, 5x, -2x and x are all linear terms. These terms are x to the first degree (X1), where the “1” isn’t written (because any number to the first power is just that number).

Terms that are not linear are called non-linear terms. The most common one you’ll come across in calculus is the quadratic term.

## Quadratic Term, Linear Term and Constant Term

Watch the video for an overview, or read on below:

A quadratic equation has the form f(x) = ax2 + bx + c, which contains three terms:

• ax2 = the quadratic term,
• bx = the linear term,
• c = the constant term.

For example, for the function f(x) = 9x2 + 3x – 5, the linear term is 3x.

Not all quadratic functions have linear terms. For example, 10x2 – 5 = 0.

## Coefficient of Linear Terms

The “3” in the above equation is the coefficient , and the “x” is the variable.

It’s possible to have more than one coefficient of a linear term. For example, the coefficient here:
f(x) = 9x2 + 3bx – 5
is 3b.

## How It Affects the Shape of Parabolas

Changing the linear term affects the vertex position, both horizontally (along the x-axis) and vertically (along the y-axis).

Increasing “b” moves the parabola down and to the left:

Decreasing “b” moves the parabola down and to the right: