Graphing Linear Equations - Best Explanation

hey what's up alright so this video is about graphing linear equations it's about graphing lines alright so I'm going to give some examples here alright I'm going to try to explain the steps so first thing we need to graph the lines we need to graph the Cartesian plane okay so Cartesian plane the XY plane is just a system of coordinates that we're going to use so here we go we have x axis right here we have a y axis right here so um the first thing you want to know about graphing a line is that there's a certain form of a linear equation which is very helpful to do so and that is slope-intercept form and the way you write that is it's y equals MX plus B this is called slope-intercept form alright and in this form you have to remember that M is the slope V is the y-intercept okay so let's say they gave us an equation alright let's say we had an equation that looked like y equals 1/2 X plus 3 now the way that I know that this is a linear equation is because it just has a single power of X this is just X to the 1 ok so I know that the graph this equation is going to look like a line now looking at slope intercept form and looking at this equation do you see how there's kind of a correspondence between these two equations so Y is y M is 1/2 X is X and B is positive 3 right ok so using that information we can use the numbers that we see here 1/2 which is the slope which is in and 3 which is the y-intercept which is B to kind of help us draw a picture of this line so the first thing you want to do is you want to look at 3 this is where you start this is the y-intercept so you say whatever this number is this is positive 3 so I'm going to put my pin right here I'm going to put a dot right there now why did I do that well the reason I put a dot on three is because this is where I would be if I counted starting from here is are you always where you start starting from here if I count it up one two three on the y-axis this is going to be my y-intercept so the reason this is called the y-intercept is because this is a place where it intercepts the y-axis okay so you start from zero and you go one two three you count upward by three if this was a negative three I would have counted downward but since it's positive I counted up where okay so there's a dot all right now what do I do with this one half turns out this 1/2 is the slope of the line and if you'll recall if you recall slope equals rise over run so if I said in this case the slope is one-half so rise over run is one-half so what this means is that I have a rise of 1 and a run of 2 see where I got this 1/2 I got this 1/2 from right here okay so the rise is 1 because it's the top number and the Run is the bottom so rise what means I put my pin on this dot and I do rise of 1 positive 1 so I go upward 1 and then I go a run of 2 so I go up 1 over 2 boom the reason I went up and right is because this is a positive number and this is a positive number so positive 1 means up negative 1 means down positive 2 would mean right like we did because this is positive and negative 2 would mean left so that's very important in terms of rise positive means up and negative means down in terms of run positive means right and negative means left okay so you got to keep that in mind because and the reason is is because this is the positive direction and this is the negative direction for X and then for y the positive directions out negative versions down so I just want to go over that ok anyways so we have our two dots okay we have our two points now um we can just simply actually just draw a line between them and that's how we will get our equation so I'm going to draw a line right here so that's the graph it's a line it has a slope of 2 because it's up 1 excuse me a slope of 1/2 because it's up 1 over 2 and it has a y-intercept of 3 because 3 is how high it is when it crosses the y-axis ok so that was one example this was easy because this equation here was already in slope intercept form it already matched up to this form when it when they gave us the equation what if we had a different sort of situation though in which we actually had to use some algebra to modify the equation a little bit and get it into slope-intercept form before we could graph it that's what I'm going to show you next ok so I'm going to draw another I draw another coordinate system another graph just so I can not have to have a try to scrunch things in so I just wanted to make this clear so here's our x-axis and our y-axis all right so now suppose if they give us an equation that looked like this what if they said ok 4x plus 2y equals negative 10 so the first thing wrong with this equation is that it needs to be in this form it needs to be in a form that looks like y equals MX plus B you can say that to yourself over and over y equals MX plus B y equals MX plus B that's you have to memorize this because this is the only form of the equation in which it makes it easy to graph the line because you can clearly see what the slope needs to be and you can clearly see what the y-intercept is going to be ok so what's the first step here to get this into slope intercept form notice what we're basically trying to do is just get Y by itself we're trying to essentially solve for y so in order to get Y by itself I need to get rid of this 4x okay so I'm going to take this 4x and I'm going to subtract it from both sides ok so I'm going to go subtracting from both sides this crosses off so my new equation simply looks like 2y equals negative 10 minus 4x okay now what I'm going to do is I still have to get rid of this positive 2 because notice see in slope-intercept for how I just have a single why I can't have any number multiplying the so I have to get rid of it so I divide by 2 divide by 2 and divide by 2 I'm dividing both sides of the equation by 2 this goes away great perfect now I have a single y this is going to be a negative 10 over positive 2 it's going to give me a negative 5 and this is going to give me a negative 4 over positive 2 is negative 2x ok final thing I'm going to do is just for cosmetic reasons I'm going to switch these two terms around okay I'm just going to say y equals negative 2x minus 5 I didn't do anything I just changed the order okay and the reason I did that is because I just want this to be more I just wanted to be more obvious that it's matching up with slope-intercept form in fact I'm going to write that underneath it so again so we can see exactly you can see exactly what this is right whoops I've just messed up supposed to be B okay so notice y equals MX plus B is corresponding 1 to 1/2 y equals negative 2x minus 5 what that means is that M and negative 2 go together and B and negative 5 go together so if I were to write this out M equals negative 2 B equals negative 5 so the slope is negative 2 and the y-intercept is negative 5 recall the first thing I'm going to do is I'm going to take my pin and I'm going to put it on the y intercept so B equals negative 5 so I'm going to start at the 0 and start at the origin I'm gonna count downward by 5 1 2 3 4 5 remember to dot the reason I counted downward is because this was a negative 5 remember last time on the first one it was positive accounted upward and this one's negative so I'm counting down okay so this is my y-intercept I know that this particular point is actually going to be a point on the equation or on the on the line okay so now the question is though is where do I go from here right well that depends on the slope recall that our slope is equal to negative 2 all right now if I were going to rewrite negative 2 in a more way in a better way to where I could see what the slope is I would rewrite it like this instead of negative 2 I'm just going to think of this as negative 2 over 1 right because anything over 1 is itself but now the reason this is important is because now I can clearly see that this is rise over run which means I have a rise of negative two and a run of positive one so if you remember so if I count downward by two and rightward by one because number down means negative and up means positive in terms of run right means positive and left means negative so negative two over one means I count downward by two rightward by one so downward by two rightward by one I'm going to put a dot right here so cool so now I have two dots and so all I do to graph the line simply draw a line to connect it to and it's going to look like this there we go so that's the graph of this line so I'm going to do a quick overview okay first thing we did is we got an equation that was already in slope-intercept form so all we had to do is we just had to look at one half and realize that it was the slope we had to look at three we realized that was the y-intercept so we put the dot here we put the dot on three we said rise over run is one over two so we went up one over two are the two dots throughout the line okay cool second example that I gave you was an equation that was not already in slope-intercept form see it didn't have a Y about itself it was all jumbled up so what I had to do is I had to do a little bit of rearranging first in order to get it to where it looked like this nice little y equals MX plus B so we got into that form funny it turned out that it was y equals negative 2x minus 5 then I looked again just like I did the first time I looked at the correspondence between M and negative 2 and B and negative 5 and so that's why I could find out I could identify by the form of this equation what him and negative 2 was excuse me what M was and what B was okay then I used that information starting with the fact that I know that this point right here is a point in the line because this is the y-intercept because it's negative 5 so I counted 5 downward and then all I did from here was I just looked at the slope I realized that negative 2 is the same as negative 2 over 1 negative 2 is the rise positive 1 is the violent so I went down to overall two points and I drew the line

Channel: BetterThanYourProf

Views: 1,293,429

Keywords: math, linear, line, lines, slope, intercept, example, examples, positive, negative, adding, subtracting, multiplying, dividing, product, sum, difference, algebra, expressions, equation, equations, solving, solve, simplifying, simplify, videos, how, sign, explained, best, explanation, grade, graders, khan, academy, formula, formulas, finding, find, what, word, number, theorem, rule, rules, integers, integer, whole, function, functions, graphing, graph, method, variable, constant, converting, rewriting, factor, factoring, y-intercept, to

Id: NAblGVxxJZo

Length: 11min 6sec (666 seconds)

Published: Thu Oct 11 2012