Chapter 1 - Section 1.3 - Linear Functions and Models - Exercises - Page 95: 127

$f+g$ is also linear, its slope is $m+n$, the sum of slopes of f and g, and its intercept is $b+c$, the sum of intercepts of f and g.

Given$\quad f(x)=mx+b,\quad g(x)=nx+c,$ $(f+g)(x)=f(x)+g(x)$ $=mx+b+nx+c$ $=(m+n)x+(b+c)$ $f+g$ is also linear, its slope is $m+n$, the sum of slopes of f and g, and its intercept is $b+c$, the sum of intercepts of f and g.