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Hey everybody Mr. Matt bog here this lesson is standard form of a linear equation so, so far we've done slope intercept form then we did point-slope form which is y minus y1 equals M times X minus x1 slope intercept as y equals MX plus B probably your favorite this one's pretty easy also don't forget all your lessons can be found at Mr. math blog comm and then at the top there's a yellow ruler at the top there's lots of classes up there your class is integrated Math one okay, so you'll find all of that stuff there, so an equation in standard form is ax plus B y equals C where a and B are not both 0 a could be 0 B could be 0 C could be 0 but a and B both can't be 0 okay and typically your book doesn't say this, but I noticed through the lesson they don't let these be fractions as your answer so if they are fractions you multiply the whole equation by the common denominator one other thing that your book doesn't say is they want this one to be positive, so I'll talk about that as we go through that they want a to be positive so anyways another thing your book doesn't say but boy this is slick right here sure cut your work down a lot if an equation is in standard form then your slope you guys is opposite the number in front of X over the number in front of Y that's your slope okay near y-intercept is just this number over this number right here okay most books including yours doesn't give you this little secret shortcut right here, but I'm going to show you the benefit of this here, so you connect never mind let's say you connect smart in your class and then, but it might frustrate your teacher I don't know how your teacher is so anyway your teacher probably knows this anyway so write an equation in standard form of each line here we go the slope is 2 and goes through negative 2 2 ok, so we want to write it in this form right here ok well if the slope is 2 ok 2 is 2 over 1 and so this 2 over 1 is opposite an over B so if I take opposite this number that's what goes in front of X and if I take B which is this one that's it goes right here should I put a 1 right there okay should be a 1 right there, but it's understood to be a 1 when there's no number there okay the only thing we got to do is find out what C is well that's where we use this ordered pair right here to figure out C so plug in negative 2 for X and positive 2 for Y, and we get C equal to 6, so there's our equation negative 2x plus y equals 6 your book that as you go through a little more of a hoops to jump through by doing your last lesson point-slope form, but that shortcut right there this one right here this is our slope it's opposite an over B so when they give you the slope man that's just quick that way so here the slope is 5 ok, and it goes through negative 2 4 well 5 over 1 again is opposite a so opposite this is a so negative 5 goes in front of X and again 1 goes in front of Y, so there's a 1 right here, and then we're going to go ahead and substitute this point in to get C ok...
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