Chapter 1 - Section 1.3 - Linear Functions and Models - Exercises - Page 95: 128

$\displaystyle \frac{f}{g}$ is not linear.

Let$\quad f(x)=mx+b,\quad g(x)=nx+c,$ Then, \quad$\displaystyle \frac{f}{g}(x)=\frac{mx+b}{nx+c}$ which, generally can not be written in linear form, $Mx+B.$ So, no, $\displaystyle \frac{f}{g}$ is not linear.