I.M. is intramuscular and that means that the API, active pharmaceutical ingredient, is only soluble in a non-polar solvent, example, oils. Which means that the injection must be in the muscle rather than on the vein because its in an oil rather than a saline solution.
If your I.V. thats intravenous meaning your API is dissolved or suspended in an aqueous solution, aka water/saline.
S.C subcutaneous. is the layer of fat that between the skin and muscle. For instance if you take your stomach and pull out the "fatty part" unless you have skin tight Abes you have some type of subconscious fat and that his where you would inject you solution wither its oil or water/saline based.
You need to dilute to whatever concentration works for you, if you 3mg/mL and you want 9mg, you inject 3mL. So your gonna dilute your ample or whatever then your just stretching your product out volumetrically.
I hope this answers your question.