Question

Does the equation represent a linear or non linear function?

$\mathrm{y}={\mathrm{x}}^2+8$

Answer 1

A linear function can be described by a linear equation and a linear equation is a degree-$1$ polynomial.

Also, a linear equation has the form: $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ where $\mathrm{m}$ is the slope, $\mathrm{c}$ is the constant.

So, $\mathrm{y}={\mathrm{x}}^2+8$ is not a linear equation because the term ${\mathrm{x}}^2$ has degree $2$.

Hence, the equation $\mathrm{y}={\mathrm{x}}^2+8$ is a non linear function.