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Slope-Intercept Form M8A

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hello and welcome to today's math video of the day the topic we're going to be talking about today is something called y equals MX plus b or also known as slope intercept form he might have heard slope intercept form before but in case you haven't here's a little bit of a lesson on slope intercept form but start with an example problem this is a linear equation how do I know it's a linear equation it looks like one an accident has a y and I can prove it let's find some points can we plug some numbers in and get some numbers out sure we can let's say we plug-in -1 in 4X and we do 4 times negative let me get a negative 3 out for why that's going to give us -3 then you can plug a zero in and get a one out and then if you plug a one-in-four times 1 plus one that's five so we've got a few points of pew pew different ordered pairs here that we could plot and once we have two or three. So we can just connect the dots everything looking good I think so so we know how to take an equation and graph that equation we can graph the equation by finding some ordered pairs by taking some input and output pairs plotting them and then connecting the dots but what I want you to notice about this function is well actually let me ask you some questions first what's the y-intercept of this line take a look at it for seconds pause the video you two up there it is you found it the Y intercept is right there and since it crosses the y-axis at one that's the y-intercept one okay probably just a coincidence that the in the equation I don't know question number 2 what is the slope of this line well take a second count the rise and the run and then you have absolutely okay yeah cuz up 4 / 1 and then up for over 1 again so the slope is for wait a second that numbers in the equation to interesting there's a 4 and a 1 and the slope is 4 Y intercept is 1 that's not a coincidence when an equation is written in y equals something X plus something those two something's will tell you the slope of the line and the y-intercept of that line they're just sitting there staring right at you you can see them you don't even have to like work to find them they're just right there but that only works when the equation is written in this format so as an example is this linear equation written in slope intercept form yes it is it's y equals something X+ something so the first something that two-thirds tells us what the slope is the slope is 2/3 and then the five tells us what the y-intercept of the line is the y-intercept is 5 so we use this formula we call it y equals MX plus b can we call it slope intercept form because if you can get your equation written in that form where the Y is all by itself on the left and then you have something X plus or minus something tagged onto the end then M the the number in the DM position rapper the slope of that line and the number in the bee position represent aware that line crosses the y-axis at why do we use m&b I've no idea who knows who cares it doesn't matter just remember y equals MX plus b is slope intercept form m is slow B is the Y intercept some more example just a really get this in your head what's the slope and y-intercept of this equation if the slope is 8 and the y-intercept is 6 how about this one can a slope be negative sure so can be negative. Mine's going to go downhill and it's going to have a y-intercept of 1 what's the slope here 3 Summits what's the y-intercept negative 11th 11 interesting so because it's a -11 we have a y-intercept that's a negative that's legal kind of makes sense right now what's the point of learning about slope in Sakonnet point is that now we can graph a linear equation without having to make an input output table all I have to do is identify the slope and the y-intercept which they're right there they're staring at me the slope is what 1/4 the Y intercept write the y-intercept is one those two numbers are just right there and once I know the slope and the y-intercept making a graph is pretty easy where should I start how about start with the Y intercept we know this line crosses the y-axis at 1 so I can put a. Right there then once I know the y-intercept I can count out the slope and put another. So my slope is 1/4 I'm just going to go up one over for put another. And now I have to do is connect the dots and I've graph that equation. That I slope intercept form yay so once you know the slope and y-intercept graphing a line is pretty easy so here's a little review of the step to composite video and write down this if you want to write it down or if it makes perfect sense already pat yourself on the back yeah alright let's sing on a graph of this line just for a little bit more practice we're using this y equals MX plus b slope intercept form at the m is negative Brianna B is for so step one was identify the slope and intercept so the slope is wet -3 but we're going to want to write that is -3/1 because remember slope is supposed to be a ratio the change in y over the change in X or the rise over the run and it helps to write it is 3/1 if it's an integer will just put it over one alright what's the Y intercept the y-intercept for it's sitting right there so how do we graph it shut up or put it up then where do we go we go down 3 because the slope is negative 3 and then forward one because it's over a positive one and then we put another day and an egg so that means it should be going downhill and we feel pretty good about ourselves because we just graft a line and it was pretty easy alright let's say you had to grab the what the what the heck man reason isn't even in slope intercept form am I supposed to find the slope and the y-intercept if it isn't in slope intercept form and slope intercept form into slope and guess what it's a good thing that we have been practicing manipulating and rearranging equations because all we have to do is just get this y by itself and then we will have it in slope-intercept form so what did I do to turn that first equation into the second one the why is still there on the left the negative 6 is still there on the right all I did is subtract 2x from both sides and why lie it is in slope intercept form so what's the slope what's the weather in if the slope is negative 2 and the y-intercept is -6 could you graph it I bet you could for the sake of time we'll just skip ad what if I gave you a line and instead of giving equation and telling you to turn it into a line I give you a line and ask you to turn it into an equation we just have to find out what's the equation for the sign if we can identify the slope and the y-intercept and we can write an equation for it what's the slope counted out he goes up three over one so the slope is three what's the y-intercept on sitting right down there at negative 5 so if I know the slope and I know the whiner I'm going to plug the slope in 4 M plug-in y-intercept in 4B and there's my equation so you can take a graph and turn it into an equation just like you can take an equation and turn it into a graph let's try one more what state for this line remember all you have to do is find the Y intercept find the slope and you will have yourself an equation going to tell you the answer to this one cuz I bet you're so smart you already figured it out alright that's all I got to say about slope intercept form today hope it all made sense we're going to be using it and practicing it a whole bunch so enjoy today's assignment

Uploaded by Jeff Marbut.

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Slope-Intercept Form M8A

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