first time math stack-exchange-er here.

I'm self-teaching single variable calculus using MIT's free online courses and I think I found a typo in the homework solution set (problem 1C-4 part d). I'm not confident enough in my own abilities to know for sure if this is a mistake vs. my poor math skills.

Could anyone tell me if the following equation is correct?

The problem is as follows: Write an equation for the tangent line for the following functions:

$$f(x) = \frac1{\sqrt{x}}\ \text{ at } x=a$$

I did the following. First I found the derivative of $f(x)$: $$f'(x) = -\frac12 x^{-\frac32}\ $$

Then I plugged in a to get $f(a)$ and $f'(a)$ and used the point-slope method to find the equation for the tangent line: $$y-a^{-\frac12} = -\frac12 a^{-\frac32}(x-a)\ $$

Which I then simplified to: $$y=-\frac12a^{-\frac32}x + \frac32 a^{-\frac12}\ $$

However, the solution set says the answer is: $$y=-a^{-\frac32}x + \frac32 a^{-\frac12}\ $$

Is the solution set correct? If so, where did the $-\frac12$ go?

Thank you!