Equation Help: Write 2x - 3y + 5 = 0 in 'y = mx + b' form

L3 said:

Hey, as almost always happens in math, I'm confused. On the math site I use, they said to rewrite the line 2x - 3y + 5 = 0 in the form y = mx + b.
So I have two questions. Through lack of knowing just how to ask my questions, I'll write out what I did.
1. 2x - 3y + 5 = 0
2. 2x - 3y + 5 - 2x = -2x
3. -3y + 5 - 5 = -2x -5

And now step four is where I had trouble. I did,

4. -3y/3 = -2x -5/3.

Now the site says the answer is y = (2/3)x + (5/3). So my two questions are, one, if you have more then one number in an equation on the right of the equals sign, then would a more correct writing be,

-3y/3 = (-2x -5)/3? The 3 divides both numbers?.....yes

in particular you should divide both sides by (-3)- as in

-3y/(-3) = (-2x-5)/(-3)

y = (2/3) * x + (5/3)

Also my second question is, when you are moving the numbers from one side of the equals sign to the other, do you always do the adding and subtracting of it first, and as in the above equation above get rid of the -3 in -3y, with division last?.... In general - yes.
I'm very sorry if this question wasn't written down very clearly.

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