problem follows, "let y be the linearisation of the function $\displaystyle f(x) = \frac{1}{x}$ at $\displaystyle x = 2$.

then y=?

they give the answer to be $\displaystyle y = - \frac{1}{4}x + 1$

I get this to be the answer

$\displaystyle

\begin{array}{l}

y = f'(a)(x - a) + f(a) \\

= - \frac{1}{4}x - 2 + \frac{1}{2} \\

= - \frac{1}{4}x - 1.5 \\

\end{array}

$

Have I done something wrong, and if so where?