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in this video we're going to take a look at writing linear equations in standard form first of all I'll be good to know what exactly standard form is so let's take a look at that standard form is ax plus B y equals C and any equation that we can write to make look like that is a linear equation now a couple more things about the a B and C they're typically standard form means that the a B and C are all integers meaning there's no fractions or decimals involved and we'll look at an example here of what we can do to get rid of those fractions also typically a is a positive number so working within those constraints we're going to take a look at five examples here of writing the linear equations in standard form the last thing is that X our excuse me that a and B cannot both be zero because if that was the case we just have C the constant so let's go ahead and take a look at this alright so first one right here this is linear because we don't have any powers or square roots or absolute values or anything like that powers other than one of course and to write it in standard form we want to make this X term be positive so to do that what I'm going to do is go ahead and add 5x to both sides because I want the x and y on the same side here so when I do that the X is positive so it's 5x plus 2y and that's equal to seven okay so took the X over there now it looks like that that's in standard form all right let's take a look at this next one now in this case notice that the X term is already positive so in order to keep it that way I'm going to leave it here and I'm going to bring the Y over so to do that I can go plus y plus y now what's left here well there's zero because I had minus y plus y there's zero then right here we have seven X plus y plus five okay and notice how I took that Y in between there because that's going to get us that standard form now I need to get rid of that five so I'm going to subtract that from both sides then zero minus five is going to be negative five and I'm going to flip it around so I'm going to take this x and y stuff and write that first so we have seven X plus y equals negative five so there it is in standard form all right let's take a look at this one next in this case notice that we've got Y terms on both sides ooh well we need to get that all together so let's take this and bring it over here so minus 3y want to get rid of those 3y so we subtract them minus 3y so that would be minus 8y equals 25 oh as that in standard form well we could write it like this if we wanted to let me just change colors here to show we would have zero X's minus 8y equals 25 okay that would look like this we just don't have an X term there so there's our standard form now sometimes we might want to know what the a B and C are because we can use those to help us find different things and that's a topic for another video...