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CCSS.Math: ,

rewrite y is equal to 2/3 x plus 4/7 in standard form the equation must be simplified which means all numbers must be integers that do not share a common factor other than one alright we'll worry about this second part in a little bit let's see if we can rewrite this so it's y equals two-thirds X plus 4/7 let me get my scratch pad out so it's y is equal to two-thirds X plus 4/7 so the way that it's written right now this is slope-intercept form it's written in the form it's written in the form Y is equal to MX plus B where m in this case is 2/3 and B is four sevens it's very easy to figure out what the slope and what the y-intercept is from this equation but we want to write this in standard form which would be the form ax plus B Y is equal to C and that extra that extra text they were saying the equation must be simplified which means all numbers must be integers that do not share a common factor other than one that just means that a B and C the in the standard form they want need to be integers and they want them to not have any common factors so if we got it to the point of say 4 X plus 2y is equal to is equal to 10 well these this number this number and this number are all divisible by two they all have the common factor of two so we would want to simplify it more divide them all by 2 and then you would get to see divide this by 2 you get 2x divide this by 2 you get plus y is equal to 5 so this is the form that they're asking for and probably because it's just easier for the site to know that this is the right answer because there's obviously a bunch of forms in this way so let's see if we can let's see if we can do that let's see if we can write it in standard form in standard form so the first thing I would want to do is well there's a bunch of ways that you could approach it the first thing you could try to do is well let's get rid of all of these let's get rid of all of these fractions and the best way to multiply rid of the fractions is to multiply by 3 and 2 x 7 if you by three you get rid of this fraction you multiply by seven you get rid of this fraction so if you multiply by three and you multiply by seven let me just rewrite it over here so actually I'll show a couple of ways that we could do this so if you multiply so one way to do it so we start with y is equal to two-thirds X plus 4/7 so if I multiply this side by three and I multiply by seven I have to do that to this side as well so this is going to be x 3 and x seven so the left-hand side becomes 21 y 21 y 3 x 7 of course is 21 we just figured that out we would distribute the 21 21 times two-thirds well see 21 divided by 3 is 7 times 2 is 14 so it's going to be 14x and then 21 divided by 7 is 3 times 4 is 12 so just like that I was able to get rid of the fractions and now let's try to get I want to get all of the I want to get the all the X's and Y's on one side so I want to get this 14x onto the left side so let's see if I can do that so I'm going to do that by it to get rid of this I would want to subtract 14x I can't just do it on the right hand side I have to do it on the left hand side as well so I want to subtract 14x and then what am I left with give myself a little bit more space so on the left hand side I have negative 14x negative 14x plus 21y plus plus 21y is equal to see I subtracted 14x to get rid of this and then I have just as equal to 12 now let's see do these am I done do these share any any is do 14 21 and 12 share any common factors let's see 14 is divisible by 2 and 7 21 is divisible by 3 and 7 12 is divided divisible by 2 6 3 4 but all of these aren't divisible by the same number 14 let's see 14 divisible by 2 so is 12 but 21 isn't 14 is divisible by 7 so is 21 but 12 isn't and yep so and 21 and 12 or divisible by 3 but 14 is it so I think this is about as simplified as I could get if there was a common factor for all three of these numbers then I would divide all of them the way I did in that in that previous example but that's not the case right over here so it's negative 14x plus 21y is equal to 12 so let me see if I can remember that and type that in so it is it is negative 14x plus 21y is equal to is equal to 12 let's see if I got it right it worked out