Should I optimize image tags in my websites' code?

Yes. Definitely. Image tags are very useful and can even bring extra traffic to your site via image searches.

An image tag or the piece of code that is used to describe what an image is when it can't be seen or isn't loaded on a site. It is not only useful for getting into image searches, but it also makes your website more accessible for your users.

To optimize your image tags correctly, We'd recommend choosing words that describe your image(s) in a more human or conversational way.  

Strict Rule:
The words need to be relevant to the image first, then the page. Do not simply stuff keywords into your image tags.