Good afternoon and welcome to the Math Video Tutor. The topic of this course is Algebra 2. You know, and I do not want you to get too afraid by the term Algebra 2, it does not mean that it is more difficult or really anymore complicated. It just means that we are going to pick up where Algebra 1 left off. And we are going to study some topics that are absolutely crucial to your understanding of other math and physics and trigonometry, geometry and things like that.
Also, I want to tell you that my goal in this course is to teach you, what you need to know to excel in algebra. In this case, in this course Algebra 2. So I am not going to cover every single topic. If you look in your book, I am not going to cover every single topic in the book. I am going to cover what I think are the most important topics. And I have decided what I believe are the most important topics based on tutoring hundreds of people and really helping people understand that.
Secondly, I like to point out that most of the time, during the video; my back is going to be to you. We are going to be working examples on the board. I am not going to do a lot of lectures where I just bore you to death with a bunch of stuff. The way to learn math, is to do, just sit there, take the examples and work is. So I am going to teach you what you need to know to take examples and work on them and I believe that through that, we will together learn algebra and hopefully get you to understand it.
So let us begin. The first topic that we are going to talk about today is linear equations, graphing and things like that. And by the way, in the course of this video series here, if there is something you do not understand, that I am going over, it is probably because the material that we are talking about maybe, was already covered in the previous course so you might want to go back and get one of my videos and other math topics if there is something I am telling you that it does not make sense.
My goal is to take it step by step by step so that no one gets lost and that is my goal today. So again, let us get started with linear equations and talk about graphing. And we will just go right to it there.
The main thing to consider is it is very important in math to do what we call a plot. Plus just talk about the basics of really what that is. I am going to draw a couple of lines here, nothing too fancy about these lines I am just going to draw a line going this way and I am going to draw a line going this way. This is called a coordinate axis. And we have to use some mechanism to label this axis so what I am going to call this, the x axis, and I am going to call this, the y axis. I mean you can label this anything you want. This could be time, this could be distance, this could be pressure of some gas, this could be volume, I mean they could be anything but in algebra, you try to keep things generally and so this is x and this y.
Okay, so what we do is we put these two lines on the board here. And then we have to start labeling some things. So I put a tick mark here and we say that is one. One here that is two, okay. Here is three, and here is four, okay. And again on the y axis, I can go one, two, and three. Of course, the number goes on up to infinity.
And likewise, for x, we have negative one, remember the number one here so you have negative numbers too. Negative three, and so on, and so this go to negative infinity and then for the y axis, you have negative one, negative two, and then go down from there.
And in the middle of course, because I am drawing this way, this is zero, this is x equal zero, and y equal zero, right in the center there. Now the only reason we label this thing, is to help us plot things. You know, you may have seen like the stock market or something like that like I will just draw a little sample here.
Maybe the stock market, the stocks goes up and down. Plots are everywhere, okay. And in this case of the stock market, it might be time of the day and like the price of stocks going up and then going down. Plots are everywhere, they are very important, they are crucial to the understanding of algebra, okay.
So this is a plot. Now, how do we use this thing? Well in general, in order to use it, I need to define what I call an ordered pair in algebra. So what I am going to do I am going to put two numbers on the board here. And just for fun I am going to say for this pair of numbers, I am going to have one comma two. Okay, when you write numbers and parenthesis, the number, then another number. The first number is always x which is this horizontal axis here.
The second number is always y, which is the axis right here. So, you always write them in terms of x first comma y, second. So it is very easy to use this. If you have a number, you take the first number and you say this is the x axis, I am going to go to number one because one is written right there. Second number is two so from this point, I am going to count up to two and I am going to put a dot right there.
This is a point on this graph x, y, go over one up two. If I have another one, let say it is three comma one, let us make it interesting, three comma negative one, I will got to go over three, and the x direction, one, two, three, and then down to negative one. So I have a point here. And I can label these points three, negative one, and of course, I can label this point one, two.
So that is the basic of how you really plot a point. That is really the just how you plot a point and all you need to remember is you have the x number first and the y number second.
Let us go and use this little bit to do, to do something a little bit more like algebra. What we are going to do is we are going to try to plot a line. Remember or maybe you do not remember but you can review right now.
This is an equation, we just pretend this is algebra one, and you never heard of a graph here. If I write something on the board, y equals x plus two, this is an equation for something. It has two variables in it. The first variable is x, the second variable is y. So, I want to find out what this looks like if I were to try to draw it here. And the way to do that is to make a table. So I make a table here. I said that is the value of x, I draw a line here, and this is the value of y. in this equation, x is what we call the independent variable. And traditionally that is how it is usually written down in algebra.
It is the number that you allow to change along this axis here and then y is just simply going to be a function of x. it is going to be dependent upon x. So, let us be talking about let just work on it.
Let us just say, we pick a few numbers here and see what happens here. Let us pretend that x is equal to one. If x is equal to one, and I put one over here, well then one plus two is three so y must equal three. When is x is one, y is equal to three. And this is going to become this point is going to become a point. Just like we are just talking about this a minute ago, I am just going to list the whole bunch of these points and we are going to draw it here.
Now, let us say x is equal to two. If x is equal to two, then y is equal to four because two plus two is four. And we just continue in here, if I put x equal three in there and three plus two is five, like that. So now, I have three points. This is a point one, three, two, four, three, five. Let us go and draw this.
One, one, two, three, and let say we have point two, four. Two is x, one two, one two, three, four is going to be up here because that is kind of off the graph here. Three, five is a perfectly the point but if you look at it, three is over here, one two, three, four, well five would just be off the chart here. So we can just pick another number that is coming in, we can say zero we can say x is equal to zero.
Zero plus two is just going to be equal to two. So here is another point, zero, two. Again zero on the x axis, and we counted two here. Now we have three points. And we can just pick another one and make it even clearer. I will pick negative one, for x, negative one plus two, remember back from your algebra is equal to one.