Meaning of Ki in Enzyme Inhibition

[blazinfury]

I am confused about the principle of Ki. I understand that Ki represents the affinity of the enzyme for the inhibitor, with a large Ki showing a strong inhibitor. In competitive inhibition, Ki serves to double the slope, while in noncompetitive inhibition Ki serves to inhibit the enzymes by 50%, but what does all of this mean in terms of applying it to a problem. I understand there there is no formula for Ki, like there is for Km, expect [E]/[EI].

 

What is the relationship between Ki and Km and can a given Ki value describe the Km magnitude if it is not given?

 

Thanks and sorry for the contorted wording of my question.