# Why is $y=f(a)+f'(a)(x-a)$ linear?

I'm reading this book: Functions of Several Variables and I didn't understand why this function is linear:

I think the authors made a mistake.

• Linear means degree 1. If 'a' is constant, then clearly it is. – Rishi Dec 3 '16 at 12:26
• This is linear with respect to $x$. Don't forget, $a$ is fixed! You can see that the slope of the line is $f'(a)$, and the y-intercept is $f(a)-af'(a)$, by expanding into the $y=mx+c$ form. – Teresa Lisbon Dec 3 '16 at 12:26
• @Rishi Right! I was thinking about the linear algebra definition of "linear" – user42912 Dec 3 '16 at 12:27
• @астонвіллаолофмэллбэрг yes I know, I was thinking about the linear algebra definition of "linear" – user42912 Dec 3 '16 at 12:28

I think the author meant "the affine function $y=f(a)+f'(a)(x-a)$" instead of "the linear function". Please have a look at this.
• It is common to refer to a function $f(x)=ax+b$ as linear, especially in high-school mathematics. – Wojowu Dec 3 '16 at 12:50