Clarifying standard form rules

we've talked about the idea of standard form of a linear equation in other videos and the point of this video is to clarify something and resolve some differences that you might see in different classes in terms of what standard form is so everyone agrees that standard form is generally a linear equation where you have some number times X plus some number times y is equal to some number so things that are in standard form would include things like 3x plus 4y is equal to 10 or 2x plus 5y is equal to negative 10 the everyone would agree that these are standard form and everyone would agree that the following are not standard standard form so if I were to write 3x is equal to negative 4y plus 10 even though these are equivalent equations this is just not in standard form similarly if I wrote that Y is equal to 3 times X plus 7 this is also not in standard form now the place where some people might disagree is if you were to see something like 6x + 8 Y is equal to 20 now why would some folks argue that this is not standard form well for some folks they would say standard form the coefficients on x and y and our constant term so our a b and c can't share any common factors and here 6 8 and 20 they are all divisible by 2 and so some folks would argue that this is not standard form and to get it into standard form you would divide all of these by 2 and if you did you would get this equation here now that's useful because then you only have one unique equation but on Khan Academy we do not restrict in that way and that is also a very popular way of thinking about it we just want you to think about it in form ax + B y is equal to C when you do the exercises on Khan Academy it's not going to be checking whether the whether these coefficients a B and C are divisible have a common have a common factor so for Khan Academy purposes this is considered standard form although don't be surprised if you encounter some folks who say no we would rather you remove any common factors now another example would be something like negative 3x minus 4y is equal to negative 10 so some folks would argue that this is not standard form because they want to see this first coefficient right over here the a being greater than 0 while here it is less than 0 for our purposes on Khan Academy we do consider this standard form but I'm just letting you know because some folks might not because this leading coefficient is not greater than 0 now another example that some people might be on the edge with would be something like one point two five x plus five point five Oh Y is equal to ten point five and the reason why some people might not consider this standard form is that a b and c are not integers some folks would say to be in standard form a b and c need to be integers and you could multiply both sides of the equation by some value that will give you integers for a b and c but for khanacademy purposes we do consider this to be in standard form and we think this is important actually not just being able to have non integers as a B or C but also being able to have a negative a right over there this negative 3 is our a and also having coefficients having our A's B's and C's having shared factors we think all that's important because sometimes the equation itself has meaning when you write it that way and we'll see that when we do when we do some word problems when we actually go into real life and we try to construct equations and based on the information it's easier to understand if you keep it in this form so for khanacademy purposes this is all standard form but it's good to be aware in your mathematical lives that some folks might want to see the restriction of no common factors between a B and C that a is greater than zero and that a B and C need to all be integers but Khan Academy does not hold you to that