Ratios in Lowest Terms FTW!!!!!!

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I need help with something. So I got this problem from my math teacher...and I have absolutely no idea what to do. 
It's relate to the graph, and algebra at the same time. 
Basically y=mx+b but switchs around like
?x - (or +) ?y (or y on it's own) =?
And when you graph them, they will either give you one solution, no solution or infinitely many solutions because with one solution the lines cross, with no solution the lines are parallel, and with infinitely many the lines are exactly the same.
TT.TT But I have no idea what to do next after you put them in y=mx+b form. The only reason why I didn't ask is because I'm too shy to speck in front the class in math class.
Please help...

CourtneyAlexander