Calculus How To

Linear Term: Definition, Examples

Share on

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:

Please accept statistics, marketing cookies to watch this video.
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:

linear term

The parabola moves down and to the left with increasing values of the linear term.

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

The parabola shifts down and to the right with decreasing values for the linear term.

This may come as a surprise: decreasing “b” moves the graph towards the positive direction on the x-axis, and increasing it will move it in the negative x-direction.


Graphing calculator on Desmos.
Quadratic Functions. Retrieved November 5, 2019 from:

Stephanie Glen. "Linear Term: Definition, Examples" From Calculus for the rest of us!

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!