using Ax + By = C  how do you put y = negative one third x + two thirds in standard form  

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Ok so the rules for standard form is that the A in Ax+By=C cannot be negative, and you must have whole numbers, or integers, for A, B, and C. y=-1/3(x)+2/3 Multiply everything by 3 so now you have 3y=-x+2 Add x to both sides and you have x+3y=2 Hope this helps!