The infographic would be hyperlinked back to your site. so when they click the graphic they get redirected to your site.

Putting a link in a picture would do nothing to help your goal of creating backlinks.

Putting a link the actual infographic wouldn't do anything more to increase your backlinks than if you added mustaches on all the faces on your infographic. :p

Ok thanks for that...so far I have a plan to submit my graphic to the infographic directories and also contact related blogs and web sites in my niche to offer them use of the infographic in exchange for them linking to my web site with the image...Is that pretty much all I need to do?

When publishing your infographic on your page you provide an embed code below it so people can conveniently republish your infographic on their site. Besides the image, usually this code contains two links: one to your original infographic page and another to the main page of your website. For example, "Keyword Infographic"-link is the courtesy of "your site name"- link.

To generate infographic embed code you can use this tool which is compatible with WordPress. Embed Code Generator from Siege Media

There are some people who will republish your infographic without any attribution - you can find them by Googling your infographic title or using Google images "Search by image". It's a good idea to reach out to them with the polite attribution reminder and usually most of them will comply with your request.

Shameless plug: for more resources, tools, tips and techniques to create a successful viral infographic, check out this forum thread or Infographic Cheat Sheet webpage.