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
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
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:
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.
Stephanie Glen. "Linear Term: Definition, Examples" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/calculus-definitions/linear-term-definition-examples/
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